Quadratic equation

Last weekend I explained the use of quadratic equation to my nephew (basically how to solve the equation). I think he understood, the concept was quite simple, if you have this:

use:

Basically, that's all you need to know at school (and probably for the rest of your life), but after spending the afternoon doing exercises I realized nobody explained my nephew WHY that formula is the solution to the quadratic equation. And then I realized that the most probable thing is that the most used formula in all high school is not well explained. Well that injustice to this beauty of maths has ended!

(this resolution is really, really, really simple!, and can be found in the Rey Pastor's book (a Spanish guy who knew something about math and wrote some books :-) )

Now we find x:

JUSTICE HAS BEEN DONE!, THE TRUTH MUST BE TOLD!

cheers!