(2x-4)(x-2)=36

Solution for (2x-4)(x-2)=36 equation:

(2x-4)(x-2)=36

We move all terms to the left:

(2x-4)(x-2)-(36)=0

We multiply parentheses ..

(+2x^2-4x-4x+8)-36=0

We get rid of parentheses

2x^2-4x-4x+8-36=0

We add all the numbers together, and all the variables

2x^2-8x-28=0

a = 2; b = -8; c = -28;
Δ = b2-4ac
Δ = -82-4·2·(-28)
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12\sqrt{2}}{2*2}=\frac{8-12\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12\sqrt{2}}{2*2}=\frac{8+12\sqrt{2}}{4}
$