100x-x^2=568.75

Solution for 100x-x^2=568.75 equation:

100x-x^2=568.75

We move all terms to the left:

100x-x^2-(568.75)=0

We add all the numbers together, and all the variables

-1x^2+100x-568.75=0

a = -1; b = 100; c = -568.75;
Δ = b2-4ac
Δ = 1002-4·(-1)·(-568.75)
Δ = 7725
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:

$\sqrt{\Delta}=\sqrt{7725}=\sqrt{25*309}=\sqrt{25}*\sqrt{309}=5\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-5\sqrt{309}}{2*-1}=\frac{-100-5\sqrt{309}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+5\sqrt{309}}{2*-1}=\frac{-100+5\sqrt{309}}{-2}
$