x(90-x)=180

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

x(90-x)=180

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(-1x+90)-180=0

We multiply parentheses

-1x^2+90x-180=0

a = -1; b = 90; c = -180;
Δ = b2-4ac
Δ = 902-4·(-1)·(-180)
Δ = 7380
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:

$\sqrt{\Delta}=\sqrt{7380}=\sqrt{36*205}=\sqrt{36}*\sqrt{205}=6\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{205}}{2*-1}=\frac{-90-6\sqrt{205}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{205}}{2*-1}=\frac{-90+6\sqrt{205}}{-2}
$