(3x-6)(x-6)=0

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

(3x-6)(x-6)=0

We multiply parentheses ..

(+3x^2-18x-6x+36)=0

We get rid of parentheses

3x^2-18x-6x+36=0

We add all the numbers together, and all the variables

3x^2-24x+36=0

a = 3; b = -24; c = +36;
Δ = b2-4ac
Δ = -242-4·3·36
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*3}=\frac{12}{6}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12}{2*3}=\frac{36}{6}
=6
$