2x(x+90)=180

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

2x(x+90)=180

We move all terms to the left:

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

We multiply parentheses

2x^2+180x-180=0

a = 2; b = 180; c = -180;
Δ = b2-4ac
Δ = 1802-4·2·(-180)
Δ = 33840
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:

$\sqrt{\Delta}=\sqrt{33840}=\sqrt{144*235}=\sqrt{144}*\sqrt{235}=12\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-12\sqrt{235}}{2*2}=\frac{-180-12\sqrt{235}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+12\sqrt{235}}{2*2}=\frac{-180+12\sqrt{235}}{4}
$