... sounds familiar... but I don't know about 'adoptive' grandparents.
I doo have a fantasy list that might have something like it...
did the cover have birthday cake? and how long was it? a few chapters or super long?
http://www.mangago.me/home/mangalist/84964/
Was the nd reincarnated into that world?
Was the mc reincarnated into that world?
http://www.mangago.me/read-manga/kenja_no_mago/
I think this one..
There's a Manga that I can't remember the name of for the life of me.
It's basically about a boy who was raised by his "Adoptive" grandparents (At least I think that bits right, can't remember entirely) who are the 2 great mages of the world, the boy is taught Magic by them, and Swordsmanship from some other guy.
He eventually gets sent off to this school where he meets a Prince an befriends him.
Oh, and this boy is like, super overpowered and enchants stuff with mad abilities.