(180-x)(x)=180

Solution for (180-x)(x)=180 equation:

(180-x)(x)=180

We move all terms to the left:

(180-x)(x)-(180)=0

We add all the numbers together, and all the variables

(-1x+180)x-180=0

We multiply parentheses

-1x^2+180x-180=0

a = -1; b = 180; c = -180;
Δ = b2-4ac
Δ = 1802-4·(-1)·(-180)
Δ = 31680
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:

$\sqrt{\Delta}=\sqrt{31680}=\sqrt{576*55}=\sqrt{576}*\sqrt{55}=24\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-24\sqrt{55}}{2*-1}=\frac{-180-24\sqrt{55}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+24\sqrt{55}}{2*-1}=\frac{-180+24\sqrt{55}}{-2}
$