P(x)=-0.2x^2+100x-3000

Solution for P(x)=-0.2x^2+100x-3000 equation:

(P)=-0.2P^2+100P-3000

We move all terms to the left:

(P)-(-0.2P^2+100P-3000)=0

We get rid of parentheses

0.2P^2-100P+P+3000=0

We add all the numbers together, and all the variables

0.2P^2-99P+3000=0

a = 0.2; b = -99; c = +3000;
Δ = b2-4ac
Δ = -992-4·0.2·3000
Δ = 7401
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{-(-99)-\sqrt{7401}}{2*0.2}=\frac{99-\sqrt{7401}}{0.4}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+\sqrt{7401}}{2*0.2}=\frac{99+\sqrt{7401}}{0.4}
$