-6x(3x-12)=0

Solution for -6x(3x-12)=0 equation:

-6x(3x-12)=0

We multiply parentheses

-18x^2+72x=0

a = -18; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·(-18)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*-18}=\frac{-144}{-36}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*-18}=\frac{0}{-36}
=0
$