(2x+2)(4x-8)=180

Solution for (2x+2)(4x-8)=180 equation:

(2x+2)(4x-8)=180

We move all terms to the left:

(2x+2)(4x-8)-(180)=0

We multiply parentheses ..

(+8x^2-16x+8x-16)-180=0

We get rid of parentheses

8x^2-16x+8x-16-180=0

We add all the numbers together, and all the variables

8x^2-8x-196=0

a = 8; b = -8; c = -196;
Δ = b2-4ac
Δ = -82-4·8·(-196)
Δ = 6336
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:

$\sqrt{\Delta}=\sqrt{6336}=\sqrt{576*11}=\sqrt{576}*\sqrt{11}=24\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-24\sqrt{11}}{2*8}=\frac{8-24\sqrt{11}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+24\sqrt{11}}{2*8}=\frac{8+24\sqrt{11}}{16}
$