(12x-12)(3x+48)=180

Solution for (12x-12)(3x+48)=180 equation:

(12x-12)(3x+48)=180

We move all terms to the left:

(12x-12)(3x+48)-(180)=0

We multiply parentheses ..

(+36x^2+576x-36x-576)-180=0

We get rid of parentheses

36x^2+576x-36x-576-180=0

We add all the numbers together, and all the variables

36x^2+540x-756=0

a = 36; b = 540; c = -756;
Δ = b2-4ac
Δ = 5402-4·36·(-756)
Δ = 400464
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:

$\sqrt{\Delta}=\sqrt{400464}=\sqrt{1296*309}=\sqrt{1296}*\sqrt{309}=36\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(540)-36\sqrt{309}}{2*36}=\frac{-540-36\sqrt{309}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(540)+36\sqrt{309}}{2*36}=\frac{-540+36\sqrt{309}}{72}
$