P(n)=-2n2+192n-3640

Solution for P(n)=-2n2+192n-3640 equation:

(P)=-2P^2+192P-3640

We move all terms to the left:

(P)-(-2P^2+192P-3640)=0

We get rid of parentheses

2P^2-192P+P+3640=0

We add all the numbers together, and all the variables

2P^2-191P+3640=0

a = 2; b = -191; c = +3640;
Δ = b2-4ac
Δ = -1912-4·2·3640
Δ = 7361
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{-(-191)-\sqrt{7361}}{2*2}=\frac{191-\sqrt{7361}}{4}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-191)+\sqrt{7361}}{2*2}=\frac{191+\sqrt{7361}}{4}
$