"managed to find out" is a correct and usable phrase in written English.
You can use it to describe having achieved something difficult or difficult-to-find information. For example: "We managed to find out the location of the missing artifacts."
"They managed to find out that I'd once got drunk at university," Hislop says.
By then, Mr Corbyn had managed to find out that a member of the cabinet had resigned.
This holiday got plenty of discussion, including editorials (against) in the local papers, though I never managed to find out precisely where on the calendar it fell.
He can hardly believe that our species has managed to find out so much about the universe using only our brains and the light that bombards our planet.
However, if you went store to store and managed to find out sales figures for 1,000 of them, you might have something closer to "material" information.
"From what I have managed to find out up until now, the legality of the procedure itself should not be disputed," Mr. Kostunica said early this morning after hours of meetings with government and army officials.
By tearing pop down to its core, they manage to find out something about the world we live in while keeping their audience in stitches.
A bizarre, 4ft-deep crater, artificially pumped full of milky, blue water, it was mainly populated by Brits and Japanese wearing armbands – I didn't manage to find out why.
Even if you manage to find out the answers on your own, you may find it difficult to stand up for yourself unless you know that your situation is wrong and that there are people to support you.
So apparently "Hypocrite" did manage to find out who a couple of these flippers were, and he cancelled their pending orders.
If you are buying the necklace as a gift, manage to find out the measurement of the gift recipient's neckline.
