The derivation of this general formula is given on the right hand side of a page, and on the left hand side of that page a specific equation is solved. The method used is exactly the same for the specific equation and the general one. The American book gets around to quadratic equations on page 650. They are first solved using a graphing calculator. Then they are solved by looking at values the function takes on as given in a table.
Factoring is next.
On page 677, the quadratic formula is stated and some plug and chug exercises are given. Then some word problems are given, so students have to translate to an equation before doing some calculations. That is it. There is no derivation of this important formula, and the tool that is usually introduced to derive it, and can be used directly on any quadratic equation and in other settings, is not introduced. It is not the American one.