n2+2n-86=3

Solution for n2+2n-86=3 equation:

n2+2n-86=3

We move all terms to the left:

n2+2n-86-(3)=0

We add all the numbers together, and all the variables

n^2+2n-89=0

a = 1; b = 2; c = -89;
Δ = b2-4ac
Δ = 22-4·1·(-89)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{10}}{2*1}=\frac{-2-6\sqrt{10}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{10}}{2*1}=\frac{-2+6\sqrt{10}}{2}
$