P(x)=40x^2+2080x-16000

Solution for P(x)=40x^2+2080x-16000 equation:

(P)=40P^2+2080P-16000

We move all terms to the left:

(P)-(40P^2+2080P-16000)=0

We get rid of parentheses

-40P^2+P-2080P+16000=0

We add all the numbers together, and all the variables

-40P^2-2079P+16000=0

a = -40; b = -2079; c = +16000;
Δ = b2-4ac
Δ = -20792-4·(-40)·16000
Δ = 6882241
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{-(-2079)-\sqrt{6882241}}{2*-40}=\frac{2079-\sqrt{6882241}}{-80}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2079)+\sqrt{6882241}}{2*-40}=\frac{2079+\sqrt{6882241}}{-80}
$