P=-0.5x2+36x-139

Solution for P=-0.5x2+36x-139 equation:

=-0.5P^2+36P-139

We move all terms to the left:

-(-0.5P^2+36P-139)=0

We get rid of parentheses

0.5P^2-36P+139=0

a = 0.5; b = -36; c = +139;
Δ = b2-4ac
Δ = -362-4·0.5·139
Δ = 1018
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-\sqrt{1018}}{2*0.5}=\frac{36-\sqrt{1018}}{1}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+\sqrt{1018}}{2*0.5}=\frac{36+\sqrt{1018}}{1}
$