(x-11)(2x+8)=180

Solution for (x-11)(2x+8)=180 equation:

(x-11)(2x+8)=180

We move all terms to the left:

(x-11)(2x+8)-(180)=0

We multiply parentheses ..

(+2x^2+8x-22x-88)-180=0

We get rid of parentheses

2x^2+8x-22x-88-180=0

We add all the numbers together, and all the variables

2x^2-14x-268=0

a = 2; b = -14; c = -268;
Δ = b2-4ac
Δ = -142-4·2·(-268)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{65}}{2*2}=\frac{14-6\sqrt{65}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{65}}{2*2}=\frac{14+6\sqrt{65}}{4}
$