Ok so i will give you the quick version of my tale... i got a calico fantail gold fish for my 5 yr old since the feeder goldfish she got at a school event died the next day.. well it out grew its little 1g mini tank we had and we decided to get a tank kit. well we grabbed a Glofish 3g led tank which is decent size for that fish at the time. only to find out that after getting that tank and 3 cardinal tetras, that i needed to cycle the tank and to watch for ammonia which the tetras died but the goldfish survived. well now im pretty good about changing the water, checking lvls, not over feeding, well we got 1 red eyed tetra and a gold mystery snail. well im fighting with cloudy water, ammonia spikes, just recently these white hair like worms (that i found out are from over feeding due to my darling daughter) and i had the original snail come out of his shell which landed him in the freezer cuz i couldnt stand watching him sick and suffer. but idk wat i need to do to better tank life. i have a decent filter, heater, gravel, fake plants, a home made aerator and yet my fish are gasping all the time, the tetra darts every now and then, but i dont see any other signs of ammonia poisoning or Ph unbalance. my city waters Ph is fairly good and my local aquarium store uses it while just adding conditioners. i know 3g tanks are like homicide for fish but its all i have for now and i am looking to make the small community i have alive and happy any thoughts?

Well, we all start somewhere.
Your 3g tank is probably only good enough for a single male Betta or a couple of shrimps.
q1: Are you serious about keeping fish?
q2: What is your budget?

At this point, you're wondering where the catch is... You're right...
Now do lots of research on the fish you'd like to keep and the tank size that you are looking at. 1g/inch of fully grown fish is about right for tropical fish but gold fish need much more - research those stocking levels too.

While goldfish are hardy, as you've experienced, keeping them in good conditions is expensive. Your little 1" goldfish can quickly outgrow the tank and fish don't stop growing based on the tank size - the organs continue growing but the length and girth of the fish stay the same... Not a good predicament is it?

The next thing is that small tanks are going to cost you MORE in the long term... Why? more problems, greater fluctuations and trouble.

A 15g is the smallest I'd suggest a beginner start with although anything up to 30g is appropriate.

Next, you need to understand the cycle and get your tank producing nitrate. The fishless cycle is a good thing but not the easiest one to get to grips with as a beginner. Your existing goldfish can be used to cycle the tank SO LONG AS YOU STAY ON TOP OF WATER PARAMETERS...

Quite frankly though, you should take your fish back to the store and think long and hard about if fish-keeping is for you. It's a great hobby but not one that you can half-heartedly do.
cb

Goldfish produce a lot of waste. I'he had trouble keeping a 30 gal clear with goldfish in it. I've also seen some huge, and I mean HUGE, goldfish. I would return the goldfish and swap it our for some other fish. IMO goldfish are best suited for a pond.

We're all lining up with bad news - sorry.
A goldfish needs 30 gallons per fish, in the medium run. They have very inefficient digestive systems, and produce a lot of waste relative to their size. Keeping a goldfish in a 3g is like keeping a cow in the bathroom.

It's a coldwater fish as well, so it should never be kept with tetras. As it grows, it will eat them.

You are fighting a losing battle.There is no way to pull off keeping a goldie in a tank that small. You actually seem to have done reasonably well, in that he/she is miraculously alive. The basic idea behind the sale of goldfish is they will die in a few weeks, since 99% of people put them in tanks that are too small. So you aren't alone in making the mistake, but unfortunately, you are doing something wrongly...

Wow I am sorry your having issues but there is a good reason why.

First off,as mentioned the poor goldfish will outgrow the tank very fast.Hes a cold water critter and not compatible with tropical fish in the long run.He can have some other gold fish companions,they are very social fish and. enjoy company.NOw if hes a common goldie he will get bigger than the fantails.The commons really are suited for ponds.Think,carp.The fancies;fantails orandas black moors,need 30 gallons as mentioned above for the first fish and ten for each after.Tankmates can be such as white cloud mountain minnows and other cold water fishes.

The tetras,need schools plain and simple.

Simply put three gallons isnt suited for really anything other than shrimp IMO.

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Thanks for all the replies guys and yes i do know about the fact that fantails need alot of room which i did not find out until after i got him and i did research on him. i am planning on getting a larger tank sometime soon and hes pretty hardy and doesn't seem to mind having a little warmer water. im more worried about the tetra i know he is a school fish but he paired with the goldie very well for the first month or so and they seemed to get along fine after he got used to a little guy swimming around. I cant give him up since that is my daughters favorite one however i may try and give up mr tetra since it is way to small to introduce anymore little guys for him. and the calico is adapting so well. however is my set up ok? besides size and school issues. Am i missing anything? and could it help the tank life to place a live (small) plant in there as well? i know my aerator is not enough with these guys. so could that help? i know that snail likes O2 rich water but im not sure if one or two small plants would be enough with all the waste and such.

i completely understand. i am not half hearted about this however i am on a budget. ever since i got this goldfish i have been forced to learn a lot about fishcare and tank life. i have done some reading up on cycling and i kinda understand it for the most part. the fish is pretty good size and i would rather give the tetra a chance at a better home then give him up i know they are messy but im up for the challenge. we cant have dogs or cats here so i want to make the most out of this for my kids. teach them responsibility, and the joy of having a beautiful successful community. i do plan on separating the fantail from the others and maybe using that 3g i have as a ER tank or med tank. i even want to go as large as a 30g and have one set up for small fish with a "jungle" as i call it and another with a rocky feel to it. i am more then willing to go the distance within my means to raise healthy and happy tank life. that and i fell in love with snails :D but i am a novice by the very definition of the word and i am eager to learn everything i can

I think you are on track, but with a too tiny tank. Given the right sized aquarium, I'd predict your approach would work well. A lot of people make the beginner's mistake (often encouraged by store personel) of mixing other fish with goldies. It's how you dig yourself out of that mess that matters, and that decides if you'll keep enjoying this hobby.
If you go into this with openness and a wish to learn, everything else is just temporary details.

Start by getting the ammonia down. I suggest something like a 50% water change every day for the next three days then go to 50% every two or three days. Do you have a test for ammonia? That would give an even better idea of how many water changes you need to do. This is not a long term fix but hopefully it will keep your fish alive for another week or two while you work out what you are going to do. It is good that you have learned about cycling a tank but in this case the tank and filter will not be big enough to support enough bacteria to take care of all the ammonia a goldfish can produce so you will always be struggling with high ammonia. The only thing you can do for now is large frequent water changes.

You certainly are not the first to end up in a situation like this and it's good that you care enough to find out what your fish need. As you realize you have some major issues that need sorting out quickly. As things stand your tank is a ticking time bomb. The only reason your fish are still alive is that you have a couple of real strong ones.

For a tank on a budget look on craigs list, freecycle, local ads etc for a second hand tank, sometimes they can be pretty cheap or even free.