(2x-22)(x+5)=180

Solution for (2x-22)(x+5)=180 equation:

(2x-22)(x+5)=180

We move all terms to the left:

(2x-22)(x+5)-(180)=0

We multiply parentheses ..

(+2x^2+10x-22x-110)-180=0

We get rid of parentheses

2x^2+10x-22x-110-180=0

We add all the numbers together, and all the variables

2x^2-12x-290=0

a = 2; b = -12; c = -290;
Δ = b2-4ac
Δ = -122-4·2·(-290)
Δ = 2464
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:

$\sqrt{\Delta}=\sqrt{2464}=\sqrt{16*154}=\sqrt{16}*\sqrt{154}=4\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{154}}{2*2}=\frac{12-4\sqrt{154}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{154}}{2*2}=\frac{12+4\sqrt{154}}{4}
$