P(x)=11.5x-0.1x^2-150

Solution for P(x)=11.5x-0.1x^2-150 equation:

(P)=11.5P-0.1P^2-150

We move all terms to the left:

(P)-(11.5P-0.1P^2-150)=0

We get rid of parentheses

0.1P^2-11.5P+P+150=0

We add all the numbers together, and all the variables

0.1P^2-10.5P+150=0

a = 0.1; b = -10.5; c = +150;
Δ = b2-4ac
Δ = -10.52-4·0.1·150
Δ = 50.25
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{-(-10.5)-\sqrt{50.25}}{2*0.1}=\frac{10.5-\sqrt{50.25}}{0.2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10.5)+\sqrt{50.25}}{2*0.1}=\frac{10.5+\sqrt{50.25}}{0.2}
$