(x-6)(3x-9)=0

Solution for (x-6)(3x-9)=0 equation:

(x-6)(3x-9)=0

We multiply parentheses ..

(+3x^2-9x-18x+54)=0

We get rid of parentheses

3x^2-9x-18x+54=0

We add all the numbers together, and all the variables

3x^2-27x+54=0

a = 3; b = -27; c = +54;
Δ = b2-4ac
Δ = -272-4·3·54
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-9}{2*3}=\frac{18}{6}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+9}{2*3}=\frac{36}{6}
=6
$