P(x)=150x-x^2

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

(P)=150P-P^2

We move all terms to the left:

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

We get rid of parentheses

P^2-150P+P=0

We add all the numbers together, and all the variables

P^2-149P=0

a = 1; b = -149; c = 0;
Δ = b2-4ac
Δ = -1492-4·1·0
Δ = 22201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22201}=149$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-149)-149}{2*1}=\frac{0}{2}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-149)+149}{2*1}=\frac{298}{2}
=149
$