P=-0.5x^2+36x-182

Solution for P=-0.5x^2+36x-182 equation:

=-0.5P^2+36P-182

We move all terms to the left:

-(-0.5P^2+36P-182)=0

We get rid of parentheses

0.5P^2-36P+182=0

a = 0.5; b = -36; c = +182;
Δ = b2-4ac
Δ = -362-4·0.5·182
Δ = 932
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{932}=\sqrt{4*233}=\sqrt{4}*\sqrt{233}=2\sqrt{233}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{233}}{2*0.5}=\frac{36-2\sqrt{233}}{1}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{233}}{2*0.5}=\frac{36+2\sqrt{233}}{1}
$