main character by accident gets into prestigious school, preferred delinquent but an idiot would be fine too. lol preferred that his behavior is shocks the whole school.

hmmm you didn't specify genre so i'm guessing any is ok?
gakuen alice is like that. the main character is sort of ditzy and noone at the school can understand why she's there at first. that part of the story is good. after that... well, i'll let you decide.
it's shojo so you've been warned if that wasn't what you were looking for!

Mx0, maybe, but I read it a long time ago and I don't remember much of it

Try Change Guy for the reverse of that situation, sort of? Hard to describe without spoilers.

Transfer Student Storm Bringer is about this, but about fighting ability not brains.

Martial Arts Hell High School?

Does Kenichi getting accepted into Ryouzanpaku count? 😉

Pretty close to OP, try Pretty Face. That seems to fit the bill both in terms of idiot and delinquent.