n^2+2n-165=0

Solution for n^2+2n-165=0 equation:

n^2+2n-165=0

a = 1; b = 2; c = -165;
Δ = b2-4ac
Δ = 22-4·1·(-165)
Δ = 664
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:

$\sqrt{\Delta}=\sqrt{664}=\sqrt{4*166}=\sqrt{4}*\sqrt{166}=2\sqrt{166}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{166}}{2*1}=\frac{-2-2\sqrt{166}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{166}}{2*1}=\frac{-2+2\sqrt{166}}{2}
$