2(2x-4)(x-4)=320

Solution for 2(2x-4)(x-4)=320 equation:

2(2x-4)(x-4)=320

We move all terms to the left:

2(2x-4)(x-4)-(320)=0

We multiply parentheses ..

2(+2x^2-8x-4x+16)-320=0

We multiply parentheses

4x^2-16x-8x+32-320=0

We add all the numbers together, and all the variables

4x^2-24x-288=0

a = 4; b = -24; c = -288;
Δ = b2-4ac
Δ = -242-4·4·(-288)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-72}{2*4}=\frac{-48}{8}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+72}{2*4}=\frac{96}{8}
=12
$