P(x)=-5x*x+400x-3000

Solution for P(x)=-5x*x+400x-3000 equation:

(P)=-5P*P+400P-3000

We move all terms to the left:

(P)-(-5P*P+400P-3000)=0

We add all the numbers together, and all the variables

P-(400P-5P*P-3000)=0

We get rid of parentheses

P-400P+5P*P+3000=0

We add all the numbers together, and all the variables

-399P+5P*P+3000=0

Wy multiply elements

5P^2-399P+3000=0

a = 5; b = -399; c = +3000;
Δ = b2-4ac
Δ = -3992-4·5·3000
Δ = 99201
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{-(-399)-\sqrt{99201}}{2*5}=\frac{399-\sqrt{99201}}{10}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-399)+\sqrt{99201}}{2*5}=\frac{399+\sqrt{99201}}{10}
$