(x-10)(-3x-12)=0

Solution for (x-10)(-3x-12)=0 equation:

(x-10)(-3x-12)=0

We multiply parentheses ..

(-3x^2-12x+30x+120)=0

We get rid of parentheses

-3x^2-12x+30x+120=0

We add all the numbers together, and all the variables

-3x^2+18x+120=0

a = -3; b = 18; c = +120;
Δ = b2-4ac
Δ = 182-4·(-3)·120
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-42}{2*-3}=\frac{-60}{-6}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+42}{2*-3}=\frac{24}{-6}
=-4
$