N=-p^2-6p+512

Solution for N=-p^2-6p+512 equation:

=-N^2-6N+512

We move all terms to the left:

-(-N^2-6N+512)=0

We get rid of parentheses

N^2+6N-512=0

a = 1; b = 6; c = -512;
Δ = b2-4ac
Δ = 62-4·1·(-512)
Δ = 2084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2084}=\sqrt{4*521}=\sqrt{4}*\sqrt{521}=2\sqrt{521}$
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{521}}{2*1}=\frac{-6-2\sqrt{521}}{2}
$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{521}}{2*1}=\frac{-6+2\sqrt{521}}{2}
$