n^2+2n-62=-6

Solution for n^2+2n-62=-6 equation:

n^2+2n-62=-6

We move all terms to the left:

n^2+2n-62-(-6)=0

We add all the numbers together, and all the variables

n^2+2n-56=0

a = 1; b = 2; c = -56;
Δ = b2-4ac
Δ = 22-4·1·(-56)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{57}}{2*1}=\frac{-2-2\sqrt{57}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{57}}{2*1}=\frac{-2+2\sqrt{57}}{2}
$