P(x)=-40x^2+1600x+2320

Solution for P(x)=-40x^2+1600x+2320 equation:

(P)=-40P^2+1600P+2320

We move all terms to the left:

(P)-(-40P^2+1600P+2320)=0

We get rid of parentheses

40P^2-1600P+P-2320=0

We add all the numbers together, and all the variables

40P^2-1599P-2320=0

a = 40; b = -1599; c = -2320;
Δ = b2-4ac
Δ = -15992-4·40·(-2320)
Δ = 2928001
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{-(-1599)-\sqrt{2928001}}{2*40}=\frac{1599-\sqrt{2928001}}{80}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1599)+\sqrt{2928001}}{2*40}=\frac{1599+\sqrt{2928001}}{80}
$