The phrase "and resolves to find" is correct and usable in written English.
It can be used when describing a decision or determination to seek out something or to discover information.
Example: "After much contemplation, she finally understands her purpose and resolves to find her true calling in life."
Alternatives: "and decides to seek" or "and commits to discovering".
When Johnson was elected in 2008 he abandoned plans to reduce the capacity to 25,000 and resolved to find a solution involving a top-flight football club that could support a larger stadium.
He had some very dicey moments, including a very close shave in Lebanon in 1983 when a knife was held to his throat, and resolved to find a less traumatic career before it was too late ("There are very few happy, old news cameramen").
The swells from the winds and waves of each storm over the last decade have come frighteningly close to drowning me but what is evident each time is that as they move over warmer and warmer waters increasing in intensity, so does my own strength and resolve to find the best in every situation.
As the UK government granted majority rule in Nyasaland and made moves towards the same in Northern Rhodesia, Smith decided that the Federation was a lost cause and resolved to found a new party that would push for Southern Rhodesian independence without an immediate transfer of power.
There are 472 Blacks in the city and Oskar resolves to find them all.
In his diaries the father had recorded his obsession with a German death-camp guard who tormented him, and his son resolves to find the man and take revenge.
After waking up in the town with a gun and contemplating suicide, she resolves to find someone.
Faith and her family have moved to a remote island for a dig that is about to happen, but she soon discovers that there are so many more reasons for why her family left the mainland… Her father's secrets and lies are everywhere, and, after a tragic incident, Faith resolves to find out the truth.
A big fan of the Sherlock Holmes mysteries, Christopher resolves to find out who killed the animal, and why.
