n^2-6n-72=-8

Solution for n^2-6n-72=-8 equation:

n^2-6n-72=-8

We move all terms to the left:

n^2-6n-72-(-8)=0

We add all the numbers together, and all the variables

n^2-6n-64=0

a = 1; b = -6; c = -64;
Δ = b2-4ac
Δ = -62-4·1·(-64)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{73}}{2*1}=\frac{6-2\sqrt{73}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{73}}{2*1}=\frac{6+2\sqrt{73}}{2}
$