(90-2x)*x=180

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

(90-2x)*x=180

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

a = -2; b = 90; c = -180;
Δ = b2-4ac
Δ = 902-4·(-2)·(-180)
Δ = 6660
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:

$\sqrt{\Delta}=\sqrt{6660}=\sqrt{36*185}=\sqrt{36}*\sqrt{185}=6\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{185}}{2*-2}=\frac{-90-6\sqrt{185}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{185}}{2*-2}=\frac{-90+6\sqrt{185}}{-4}
$