n^2-8n-56=0

Solution for n^2-8n-56=0 equation:

n^2-8n-56=0

a = 1; b = -8; c = -56;
Δ = b2-4ac
Δ = -82-4·1·(-56)
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{-(-8)-12\sqrt{2}}{2*1}=\frac{8-12\sqrt{2}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12\sqrt{2}}{2*1}=\frac{8+12\sqrt{2}}{2}
$