x=-0.5x^2+36x-198

Solution for x=-0.5x^2+36x-198 equation:

x=-0.5x^2+36x-198

We move all terms to the left:

x-(-0.5x^2+36x-198)=0

We get rid of parentheses

0.5x^2-36x+x+198=0

We add all the numbers together, and all the variables

0.5x^2-35x+198=0

a = 0.5; b = -35; c = +198;
Δ = b2-4ac
Δ = -352-4·0.5·198
Δ = 829
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{-(-35)-\sqrt{829}}{2*0.5}=\frac{35-\sqrt{829}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{829}}{2*0.5}=\frac{35+\sqrt{829}}{1}
$