x=-x^2+20x-64

Solution for x=-x^2+20x-64 equation:

x=-x^2+20x-64

We move all terms to the left:

x-(-x^2+20x-64)=0

We get rid of parentheses

x^2-20x+x+64=0

We add all the numbers together, and all the variables

x^2-19x+64=0

a = 1; b = -19; c = +64;
Δ = b2-4ac
Δ = -192-4·1·64
Δ = 105
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{-(-19)-\sqrt{105}}{2*1}=\frac{19-\sqrt{105}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{105}}{2*1}=\frac{19+\sqrt{105}}{2}
$