(x-6)(2x-6)=20x

Solution for (x-6)(2x-6)=20x equation:

(x-6)(2x-6)=20x

We move all terms to the left:

(x-6)(2x-6)-(20x)=0

We add all the numbers together, and all the variables

-20x+(x-6)(2x-6)=0

We multiply parentheses ..

(+2x^2-6x-12x+36)-20x=0

We get rid of parentheses

2x^2-6x-12x-20x+36=0

We add all the numbers together, and all the variables

2x^2-38x+36=0

a = 2; b = -38; c = +36;
Δ = b2-4ac
Δ = -382-4·2·36
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-34}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+34}{2*2}=\frac{72}{4}
=18
$