You don't convince them of anything. If you want to move out to go to university, you are 18, an adult, and as such fully responsible for yourself at that age. You don't there consent. Nobody can legally stop you if you wished to walk out, and the university you go to would laugh if your parents did attempt to stop you going.
Of course, they may not be pleased about that. They could ruin your relationship, but that's on them.