Can a Beta????

Yes, you can put them together. 75F is a good temperature for both to live well. Goldfish are really not cold water fish as people think, its just that they don't necessarily need heat to survive, but they do thrive in warm water better than cold. You would need at least a 70 gallon tank for those fish to live long healthy lives.

75 degrees is getting too warm for goldfish. for a tank with 6 goldfish you're looking for at least a 60 gallon tank, and even that would be a bit on the tiny side. you haven't said how large your tank is.

tropical fish and goldfish do NOT mix at all. and when the goldfish get bigger they may eat any smaller fish in the tank. i'd be surprised if the corys live much longer in that tank, as they hang out on the bottom they're going to succumb to the goldfishes constant waste production and ammonia levels quicker than other fish.

there are a few species of corys that can cope in cooler waters, but not with goldfish at all.

i'm concerned you have a sucker fish, this label can be applied to dozens and dozens of fish. if its a Chinese Algae Eater, it will suck on your goldfish, if it's Plec they may also do this too. They're also tropical fish and shouldn't be kept with goldfish. Plecs can grow anything from 4"-24" so IDing what you have is important!

So what size tank is this? I think you're going to need to do some rehoming before you consider any other fish!

No because 3 issues. Its no longer filtered Its no longer heated Its no longer even sufficiently massive for the only you've. in case you inquire from me and maximum different fish proprietors something a lot less that 5 gallons shouldn't in any respect homestead any fish, even a Betta. The male will little doubt beat up the female in one of those small bowl without position to pass. sturdy success

Betta fish need warmer water than goldfish (between 22 and 29deg C) so if your tank is warm enough for a betta, it's to hot for the goldfish and vice versa.

goldfish and bettas don't mix by personality. male goldfish will chase and nip just about anything. this could result in a dead betta or your betta might fight back and you will have a dead goldfish. its a lose-lose mix. females won't fare any better. bettas don't like being chased and nipped.

you can put beta in with almost any fish that it can't swallow. You can have as many females as you like but you can only have one male