Swede, could you please take a shot of the fancy goldfish that you are dealing with? A 30g is about the minimum I would advise for fancy goldfish but it also depends which variant we are talking about because several can reach 10-12 inches max. A 30g can house two fancy types. If these were crown pearlscales, bubble eyes, celestials, eggfish or shortbodied orandas, a 30g will suit to just fine.
Since goldfish are very sociable creatures, it would be more prudent to provide them their company preferably their own. One alone tends to not do anything much but sulk looking rather depressed due to lack of interaction with members of its own species. I have one that has remained isolated for his own sake after the tumor surgery and I sometimes find myself sympathetic since he looks depressed without anyone to interact with but he appreciates how I spend time to feed him and even check his condition. He's not the type who would freak out from the presence of their owners but rather hold still when petted.
Fancy goldies can tolerate a temperature bracket of 72-78 degrees but make sure not to exceed it anymore because at that point, they tend to gasp to the surface. Goldfish are heavy oxygen consumers so you have to avoid that issue.
What tetras do you have? Some tetras may work just fine but you have to avoid fin nippers in general. The only tankmates I ever considered with goldfish are platies, guppies, bristlenose plecos and dojo loaches aside from the obvious apple snails.