P(x)=-40x2+2000x-16,000

Solution for P(x)=-40x2+2000x-16,000 equation:

(P)=-40P^2+2000P-16.000

We move all terms to the left:

(P)-(-40P^2+2000P-16.000)=0

We get rid of parentheses

40P^2-2000P+P+16.000=0

We add all the numbers together, and all the variables

40P^2-1999P+16=0

a = 40; b = -1999; c = +16;
Δ = b2-4ac
Δ = -19992-4·40·16
Δ = 3993441
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{-(-1999)-\sqrt{3993441}}{2*40}=\frac{1999-\sqrt{3993441}}{80}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1999)+\sqrt{3993441}}{2*40}=\frac{1999+\sqrt{3993441}}{80}
$