I'm going to leave the girl I was seeing without properly telling her
Why not just tell her that the relationship is over?
She was mad at me for cheating on her
Ghosting someone like that is a horrible thing to do.  People want closure and you should give it to her.
Why should I? What will it solve?
It is going to save her a lot of questioning herself. It is expected that you tell someone when you are done with the relationship with them.