(15x-31)(9x+11)=180

Solution for (15x-31)(9x+11)=180 equation:

(15x-31)(9x+11)=180

We move all terms to the left:

(15x-31)(9x+11)-(180)=0

We multiply parentheses ..

(+135x^2+165x-279x-341)-180=0

We get rid of parentheses

135x^2+165x-279x-341-180=0

We add all the numbers together, and all the variables

135x^2-114x-521=0

a = 135; b = -114; c = -521;
Δ = b2-4ac
Δ = -1142-4·135·(-521)
Δ = 294336
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:

$\sqrt{\Delta}=\sqrt{294336}=\sqrt{576*511}=\sqrt{576}*\sqrt{511}=24\sqrt{511}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-24\sqrt{511}}{2*135}=\frac{114-24\sqrt{511}}{270}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+24\sqrt{511}}{2*135}=\frac{114+24\sqrt{511}}{270}
$