Hey I have 50l aquarium with 2 goldfish, temperature is always 25°C and my question is will they survive without filter?
A 50 liters tank is too small for you to keep goldfish, and even more so if you do not have any filtration.
The most important thing for fish to survive in an unfiltered tank is the water's surface area being in contact with the air, the larger the surface is the more oxygen will get into the water and more CO2 will get out.
Goldfish is a coldwater fish and if you keep the temparature below about 20 degrees Celsius, the water will be able to hold more oxygen than warmer water will do,this makes it easier to keep the fish alive.
You will have problems keeping a small tank in biological balance if you do not have any type of filtration. Waste products will absorb a lot of oxygen and this might bring the oxygen level down and kill your fish.
I do not suggest you putting fish into the tank before you get proper filtration going so the waste products can be broken down and the water get well oxygenated.
If you put them into the water and let them be: no, they will not survive.
But if you make the effort and perform partial water changes once every few days, then they could survive long and happy.
The excretions of the fish and decomposing uneaten food make the water dirty and even toxic. Someone (you or the filter) has to clean it.
If you have no plants, there is a second point: oxygen. The fish need it to breath in the water. If it is gone then something have to make new. Plants do this, or falling water (for example if you let the water from filter drop into the tank) brings air bubbles under the surface. There are also air pumps, but if you do not have a filter, I assume you do not use a air pump.
Yes your fish could survive providing you put a lot of work in doing 30 to 50% water changes however to have a healthy tank you really should have filter,pump,plants etc so your filter grows beneficial bacteria which will turn ammonia to nitrite then nitrite to nitrate then you only need deal with the nitrates by doing partial water changes. Do you use water conditioner when you fill your tank up with clean water as your fish won't last 2 minutes if you don't. Do some research there's plenty of information out there.
I would say aeration is the most important single factor, especially because 25 C is pretty warm for goldfish. The warmer the water ,the less oxygen it has. Changing water is good but I don't do it much unless I am trying to breed something. Filtering is good but not essential; siphon debris off the bottom occasionally. I love plants , floaters are very easy. As bacteria break down fish wastes , nitrogen compounds are produced which is just what the plants absorb. And gold fish like to nibble plants : The basis on a" balanced aquarium " - Fish produce nitrogenous waste > plants absorb nitrogenous matter and grow > fish eat plants.