(X+15)(4x-20)=180

Solution for (X+15)(4x-20)=180 equation:

(X+15)(4X-20)=180

We move all terms to the left:

(X+15)(4X-20)-(180)=0

We multiply parentheses ..

(+4X^2-20X+60X-300)-180=0

We get rid of parentheses

4X^2-20X+60X-300-180=0

We add all the numbers together, and all the variables

4X^2+40X-480=0

a = 4; b = 40; c = -480;
Δ = b2-4ac
Δ = 402-4·4·(-480)
Δ = 9280
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:

$\sqrt{\Delta}=\sqrt{9280}=\sqrt{64*145}=\sqrt{64}*\sqrt{145}=8\sqrt{145}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{145}}{2*4}=\frac{-40-8\sqrt{145}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{145}}{2*4}=\frac{-40+8\sqrt{145}}{8}
$