P(x)=300x-25x2

Solution for P(x)=300x-25x2 equation:

(P)=300P-25P^2

We move all terms to the left:

(P)-(300P-25P^2)=0

We get rid of parentheses

25P^2-300P+P=0

We add all the numbers together, and all the variables

25P^2-299P=0

a = 25; b = -299; c = 0;
Δ = b2-4ac
Δ = -2992-4·25·0
Δ = 89401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{89401}=299$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-299)-299}{2*25}=\frac{0}{50}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-299)+299}{2*25}=\frac{598}{50}
=11+24/25
$