-X^2+200x=180

Solution for -X^2+200x=180 equation:

-X^2+200X=180

We move all terms to the left:

-X^2+200X-(180)=0

We add all the numbers together, and all the variables

-1X^2+200X-180=0

a = -1; b = 200; c = -180;
Δ = b2-4ac
Δ = 2002-4·(-1)·(-180)
Δ = 39280
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:

$\sqrt{\Delta}=\sqrt{39280}=\sqrt{16*2455}=\sqrt{16}*\sqrt{2455}=4\sqrt{2455}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-4\sqrt{2455}}{2*-1}=\frac{-200-4\sqrt{2455}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+4\sqrt{2455}}{2*-1}=\frac{-200+4\sqrt{2455}}{-2}
$