Yes this is correct. Don't use "find out" in this example.
Scientists are trying to find a cure for cancer
"a cure" is a noun, and it's a thing which can be found. It may not be a physical object, so to speak, but it's still a noun. You can nearly always use to find + noun. One can "find love", or "find happiness" too!
"To find out" means "to ascertain/discern" or "to discover information (about someone/something". There is a sense here of attempting to get to the truth, or find a definitive answer/information about someone/something.
"Find out" is usually followed by the words: that, if, how, when, where, what, who, why, etc. Sometimes "that" can be omitted, but it's still implied. Also note that "find out" is quite informal, but it is commonly used in everyday English.
It took me several days to find out [that] she was sick.
They want to find out who he is.
The government must find out why this has happened.
The police are trying to find out if a murder has been committed.
Astronomers are trying to find out how old the universe is.
It's also possible to say "to find someone/something out". This means to reveal the truth about someone/something.