n^2-16n=8

Solution for n^2-16n=8 equation:

n^2-16n=8

We move all terms to the left:

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}
$