P=-0.5x^2+36x-234

Solution for P=-0.5x^2+36x-234 equation:

=-0.5P^2+36P-234

We move all terms to the left:

-(-0.5P^2+36P-234)=0

We get rid of parentheses

0.5P^2-36P+234=0

a = 0.5; b = -36; c = +234;
Δ = b2-4ac
Δ = -362-4·0.5·234
Δ = 828
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:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{23}}{2*0.5}=\frac{36-6\sqrt{23}}{1}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{23}}{2*0.5}=\frac{36+6\sqrt{23}}{1}
$