(4x-60)(x+20)=180

Solution for (4x-60)(x+20)=180 equation:

(4x-60)(x+20)=180

We move all terms to the left:

(4x-60)(x+20)-(180)=0

We multiply parentheses ..

(+4x^2+80x-60x-1200)-180=0

We get rid of parentheses

4x^2+80x-60x-1200-180=0

We add all the numbers together, and all the variables

4x^2+20x-1380=0

a = 4; b = 20; c = -1380;
Δ = b2-4ac
Δ = 202-4·4·(-1380)
Δ = 22480
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:

$\sqrt{\Delta}=\sqrt{22480}=\sqrt{16*1405}=\sqrt{16}*\sqrt{1405}=4\sqrt{1405}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{1405}}{2*4}=\frac{-20-4\sqrt{1405}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{1405}}{2*4}=\frac{-20+4\sqrt{1405}}{8}
$