I deleted an answer which had no upvotes or downvotes, but after some time I saw that my reputation was -2 and the reason is linked to my search engine.
I want to know why this happened and what "linked to my serach engine" means?
This is unrelated to the answer you deleted.
You suggested an edit to a question titled "linked to my serach engine"[sic] (10k-only link), and the suggestion was accepted, gaining you two rep points.
The question was later closed, then deleted by three other users (Charles, Mat, and John Saunders). The two rep from your edit was removed along with the question.