(X-12)(2x+15)=180

Solution for (X-12)(2x+15)=180 equation:

(X-12)(2X+15)=180

We move all terms to the left:

(X-12)(2X+15)-(180)=0

We multiply parentheses ..

(+2X^2+15X-24X-180)-180=0

We get rid of parentheses

2X^2+15X-24X-180-180=0

We add all the numbers together, and all the variables

2X^2-9X-360=0

a = 2; b = -9; c = -360;
Δ = b2-4ac
Δ = -92-4·2·(-360)
Δ = 2961
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:

$\sqrt{\Delta}=\sqrt{2961}=\sqrt{9*329}=\sqrt{9}*\sqrt{329}=3\sqrt{329}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{329}}{2*2}=\frac{9-3\sqrt{329}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{329}}{2*2}=\frac{9+3\sqrt{329}}{4}
$