how do know if the gold fish in the tank is healthy or not?

Goldfish may be coldwater fish, but this does not mean they can tolerate rapid changes in temperature. The sudden shift in temperature that comes at night, for example in an office building where a goldfish might be kept in a small office tank, could kill them, especially in winter. Temperatures under about 10 °C (50 °F) are dangerous to goldfish. Conversely, temperatures over 25 °C (77 °F) can be extremely damaging for goldfish (this is the main reason why they shouldn't be kept in tropical tanks).[9]

The popular image of a goldfish in a small fishbowl is an enduring one. Unfortunately, the risk of stunting, deoxygenation, ammonia/nitrite poisoning caused by such a small environment means that this is hardly a suitable home for any species of fish, and some countries have banned the sale of bowls of that type under animal rights legislation.[10]

The supposed reputation of goldfish dying quickly is often due to poor care amongst uninformed buyers looking for a cheap pet.[11] The true lifespan of a well-cared-for goldfish in captivity can extend beyond 10 years.

Goldfish, like all fish that are kept as pets, do not like to be petted. In fact, touching a goldfish can be quite dangerous to its health, as it can cause the protective slime coat to be damaged or removed, which opens the fish’s skin up to infection from bacteria or parasites in the water.