(2x-4)(x-2)=12x+8

Solution for (2x-4)(x-2)=12x+8 equation:

(2x-4)(x-2)=12x+8

We move all terms to the left:

(2x-4)(x-2)-(12x+8)=0

We get rid of parentheses

(2x-4)(x-2)-12x-8=0

We multiply parentheses ..

(+2x^2-4x-4x+8)-12x-8=0

We get rid of parentheses

2x^2-4x-4x-12x+8-8=0

We add all the numbers together, and all the variables

2x^2-20x=0

a = 2; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·2·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*2}=\frac{40}{4}
=10
$