(2x-90)(x+60)=180

Solution for (2x-90)(x+60)=180 equation:

(2x-90)(x+60)=180

We move all terms to the left:

(2x-90)(x+60)-(180)=0

We multiply parentheses ..

(+2x^2+120x-90x-5400)-180=0

We get rid of parentheses

2x^2+120x-90x-5400-180=0

We add all the numbers together, and all the variables

2x^2+30x-5580=0

a = 2; b = 30; c = -5580;
Δ = b2-4ac
Δ = 302-4·2·(-5580)
Δ = 45540
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:

$\sqrt{\Delta}=\sqrt{45540}=\sqrt{36*1265}=\sqrt{36}*\sqrt{1265}=6\sqrt{1265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{1265}}{2*2}=\frac{-30-6\sqrt{1265}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{1265}}{2*2}=\frac{-30+6\sqrt{1265}}{4}
$