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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+2x^2-60x+60x-1800)-180=0

We get rid of parentheses

2x^2-60x+60x-1800-180=0

We add all the numbers together, and all the variables

2x^2-1980=0

a = 2; b = 0; c = -1980;
Δ = b2-4ac
Δ = 02-4·2·(-1980)
Δ = 15840
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:

$\sqrt{\Delta}=\sqrt{15840}=\sqrt{144*110}=\sqrt{144}*\sqrt{110}=12\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{110}}{2*2}=\frac{0-12\sqrt{110}}{4}
=-\frac{12\sqrt{110}}{4}
=-3\sqrt{110}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{110}}{2*2}=\frac{0+12\sqrt{110}}{4}
=\frac{12\sqrt{110}}{4}
=3\sqrt{110}
$