(4x+20)(2x-20)=180

Solution for (4x+20)(2x-20)=180 equation:

(4x+20)(2x-20)=180

We move all terms to the left:

(4x+20)(2x-20)-(180)=0

We multiply parentheses ..

(+8x^2-80x+40x-400)-180=0

We get rid of parentheses

8x^2-80x+40x-400-180=0

We add all the numbers together, and all the variables

8x^2-40x-580=0

a = 8; b = -40; c = -580;
Δ = b2-4ac
Δ = -402-4·8·(-580)
Δ = 20160
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:

$\sqrt{\Delta}=\sqrt{20160}=\sqrt{576*35}=\sqrt{576}*\sqrt{35}=24\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-24\sqrt{35}}{2*8}=\frac{40-24\sqrt{35}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+24\sqrt{35}}{2*8}=\frac{40+24\sqrt{35}}{16}
$