-12(x-10)x=0

Solution for -12(x-10)x=0 equation:

-12(x-10)x=0

We multiply parentheses

-12x^2+120x=0

a = -12; b = 120; c = 0;
Δ = b2-4ac
Δ = 1202-4·(-12)·0
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-120}{2*-12}=\frac{-240}{-24}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+120}{2*-12}=\frac{0}{-24}
=0
$