P=2n2-40n-165

Solution for P=2n2-40n-165 equation:

=2P^2-40P-165

We move all terms to the left:

-(2P^2-40P-165)=0

We get rid of parentheses

-2P^2+40P+165=0

a = -2; b = 40; c = +165;
Δ = b2-4ac
Δ = 402-4·(-2)·165
Δ = 2920
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2920}=\sqrt{4*730}=\sqrt{4}*\sqrt{730}=2\sqrt{730}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{730}}{2*-2}=\frac{-40-2\sqrt{730}}{-4}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{730}}{2*-2}=\frac{-40+2\sqrt{730}}{-4}
$