6x*(x-6)=0

Solution for 6x*(x-6)=0 equation:

6x(x-6)=0

We multiply parentheses

6x^2-36x=0

a = 6; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·6·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*6}=\frac{72}{12}
=6
$