The phrase "actually discovered that" is correct and usable in written English.
It can be used when you want to emphasize the reality or truth of a finding or realization.
Example: "After extensive research, we actually discovered that the initial hypothesis was incorrect."
Alternatives: "truly found that" or "really uncovered that".
He suggested, long before toxins were actually discovered, that some bacteria might produce these substances.
It was Berryman, she recalled in "Reversals," who actually discovered that she was dyslexic, after she had written him a note: "Deare/ Time for olny a hurried note... Swimming every day despite gary skies.
Is it any wonder that a University of Virginia-led study (11 studies, actually) discovered that participants would rather face electric shock than sit quietly alone with their thoughts for six to 15 minutes?
Everybody was enjoying the fireworks and I actually discovered that Icelandic people have quite a love and obsession for them.
In fact, the site says over 80% of online daters have suspected that the profile images being used online are fakes and over a third have actually discovered that a person's identity does not match that of their online persona.
Although we had hypothesized that deceivers would use more swear words as an attempt to appear more credible through a faked emotional response, we actually discovered that truth tellers used more extreme swearing (the mean for truthful swearing = .0652; the mean for deceptive swearing = .0000).0000
The mother, shrouded in conditions of absolute secrecy, the announcement unable to be said aloud until the security of the 13th week, lest anyone actually discover that the embryo did not survive to the second trimester.
I think I also read recently in L'Equipe that Juventus have instigated a season ticket for women which works out at about £1 per league game and not much more for Champions League fixtures, although it would be too depressing to actually discover that this is true" - Paul Stump.
So when he sings for her, and she dances for him, they're actually discovering that about each other at the exact same moment that the characters are discovering that about each other, at the exact same moment that the audience is.
Scientists are actually discovering that sleep plays an absolutely vital role in keeping your brain healthy.
Although all these things are only games and may sound silly to you, you might actually discover that you won't be able to solve them as soon as you start, since they're specifically made to tease the brain and let you out of your comfort zone.
