200x-x^2=9900

Solution for 200x-x^2=9900 equation:

200x-x^2=9900

We move all terms to the left:

200x-x^2-(9900)=0

We add all the numbers together, and all the variables

-1x^2+200x-9900=0

a = -1; b = 200; c = -9900;
Δ = b2-4ac
Δ = 2002-4·(-1)·(-9900)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-20}{2*-1}=\frac{-220}{-2}
=+110
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+20}{2*-1}=\frac{-180}{-2}
=+90
$