(2x-30)(x+60)=180

Solution for (2x-30)(x+60)=180 equation:

(2x-30)(x+60)=180

We move all terms to the left:

(2x-30)(x+60)-(180)=0

We multiply parentheses ..

(+2x^2+120x-30x-1800)-180=0

We get rid of parentheses

2x^2+120x-30x-1800-180=0

We add all the numbers together, and all the variables

2x^2+90x-1980=0

a = 2; b = 90; c = -1980;
Δ = b2-4ac
Δ = 902-4·2·(-1980)
Δ = 23940
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:

$\sqrt{\Delta}=\sqrt{23940}=\sqrt{36*665}=\sqrt{36}*\sqrt{665}=6\sqrt{665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{665}}{2*2}=\frac{-90-6\sqrt{665}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{665}}{2*2}=\frac{-90+6\sqrt{665}}{4}
$