Here’s a snapshot of the derivation of the quadratic formula from the blackboard on Friday:

(Note that my “blackboard management” wasn’t ideal: the derivation starts in the middle board and the continues on LHS board. The RHS board has a numerical example, which follows the same steps as the general derivation.)

Also, here is PatrickJMT’s 7min video going thru the derivation:

You can also read the derivation on the Wikipedia page for the quadratic formula, or in Sec 7.2 of the textbook (p592).