'discover the answer' is correct and can be used in written English.
For example, you could use it in a how-to article: "Follow these steps to discover the answer to your question."
You also discover the answer to that all-important question, how do you go to the toilet in a blizzard?
In the process, the rest of the world came to discover the answer to, What's a Hockeyroo?
To discover the answer, Terrace thrusts Nim into the bosom of a willing colleague's rich, hippy household in New York.
So, this playful master of avant-garde food was experimenting to discover the answer: taking the dish apart, then putting it back together.
It's great to go to the labyrinth with a question in mind, and discover the answer while circling the soft grass in your bare feet.
Hmm? Blue Peter?" before reverting to Wikipedia to discover the answer is: no, she's from several other Channel 4 shows about superfoods.
Consult the U.S. General Accounting Office and/or any government contractors to discover the answers to these questions, and write a report of your findings.
He was then already fascinated with what he calls the "mystery of human life" — where did we come from and why? — and hoped that in the ancient civilizations, he might discover the answers he sought.
Upon graduating from Yale in 2004, I sought to discover the answers for myself and shocked my family and friends by moving to Israel and enlisting in the Israel Defense Forces.
