Databases do not use binary trees for indexes and tables, they use B-trees. B-trees are a family of self balancing tree data structures which usually are not binary because in a database you want the tree to have few levels.
Thank you. I remembe having to balance a B-Tree in my DB final. 5 nodes deep. Had to show all of the work. I think it ended up with 20 some revisions based on all the insert and delete statements.