(x)=-x2+200x-8500

Solution for (x)=-x2+200x-8500 equation:

(x)=-x2+200x-8500

We move all terms to the left:

(x)-(-x2+200x-8500)=0

We add all the numbers together, and all the variables

-(-1x^2+200x-8500)+x=0

We get rid of parentheses

1x^2-200x+x+8500=0

We add all the numbers together, and all the variables

x^2-199x+8500=0

a = 1; b = -199; c = +8500;
Δ = b2-4ac
Δ = -1992-4·1·8500
Δ = 5601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-199)-\sqrt{5601}}{2*1}=\frac{199-\sqrt{5601}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-199)+\sqrt{5601}}{2*1}=\frac{199+\sqrt{5601}}{2}
$