n^2-4n-52=8

Solution for n^2-4n-52=8 equation:

n^2-4n-52=8

We move all terms to the left:

n^2-4n-52-(8)=0

We add all the numbers together, and all the variables

n^2-4n-60=0

a = 1; b = -4; c = -60;
Δ = b2-4ac
Δ = -42-4·1·(-60)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16}{2*1}=\frac{-12}{2}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16}{2*1}=\frac{20}{2}
=10
$