x(x-18)-6(x-18)=0

Solution for x(x-18)-6(x-18)=0 equation:

x(x-18)-6(x-18)=0

We multiply parentheses

x^2-18x-6x+108=0

We add all the numbers together, and all the variables

x^2-24x+108=0

a = 1; b = -24; c = +108;
Δ = b2-4ac
Δ = -242-4·1·108
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12}{2*1}=\frac{12}{2}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12}{2*1}=\frac{36}{2}
=18
$