n^2-13n-15=53

Solution for n^2-13n-15=53 equation:

n^2-13n-15=53

We move all terms to the left:

n^2-13n-15-(53)=0

We add all the numbers together, and all the variables

n^2-13n-68=0

a = 1; b = -13; c = -68;
Δ = b2-4ac
Δ = -132-4·1·(-68)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-21}{2*1}=\frac{-8}{2}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+21}{2*1}=\frac{34}{2}
=17
$