n^2+16n-2=6

Solution for n^2+16n-2=6 equation:

n^2+16n-2=6

We move all terms to the left:

n^2+16n-2-(6)=0

We add all the numbers together, and all the variables

n^2+16n-8=0

a = 1; b = 16; c = -8;
Δ = b2-4ac
Δ = 162-4·1·(-8)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-12\sqrt{2}}{2*1}=\frac{-16-12\sqrt{2}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+12\sqrt{2}}{2*1}=\frac{-16+12\sqrt{2}}{2}
$