(x-15)(3x+5)=180

Solution for (x-15)(3x+5)=180 equation:

(X-15)(3X+5)=180

We move all terms to the left:

(X-15)(3X+5)-(180)=0

We multiply parentheses ..

(+3X^2+5X-45X-75)-180=0

We get rid of parentheses

3X^2+5X-45X-75-180=0

We add all the numbers together, and all the variables

3X^2-40X-255=0

a = 3; b = -40; c = -255;
Δ = b2-4ac
Δ = -402-4·3·(-255)
Δ = 4660
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:

$\sqrt{\Delta}=\sqrt{4660}=\sqrt{4*1165}=\sqrt{4}*\sqrt{1165}=2\sqrt{1165}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{1165}}{2*3}=\frac{40-2\sqrt{1165}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{1165}}{2*3}=\frac{40+2\sqrt{1165}}{6}
$