(4x+20)(x-10)=180

Solution for (4x+20)(x-10)=180 equation:

(4x+20)(x-10)=180

We move all terms to the left:

(4x+20)(x-10)-(180)=0

We multiply parentheses ..

(+4x^2-40x+20x-200)-180=0

We get rid of parentheses

4x^2-40x+20x-200-180=0

We add all the numbers together, and all the variables

4x^2-20x-380=0

a = 4; b = -20; c = -380;
Δ = b2-4ac
Δ = -202-4·4·(-380)
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-36\sqrt{5}}{2*4}=\frac{20-36\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+36\sqrt{5}}{2*4}=\frac{20+36\sqrt{5}}{8}
$