(x-2)(2x-4)=288

Solution for (x-2)(2x-4)=288 equation:

(x-2)(2x-4)=288

We move all terms to the left:

(x-2)(2x-4)-(288)=0

We multiply parentheses ..

(+2x^2-4x-4x+8)-288=0

We get rid of parentheses

2x^2-4x-4x+8-288=0

We add all the numbers together, and all the variables

2x^2-8x-280=0

a = 2; b = -8; c = -280;
Δ = b2-4ac
Δ = -82-4·2·(-280)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-48}{2*2}=\frac{-40}{4}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+48}{2*2}=\frac{56}{4}
=14
$