n^2-18n-61=2

Solution for n^2-18n-61=2 equation:

n^2-18n-61=2

We move all terms to the left:

n^2-18n-61-(2)=0

We add all the numbers together, and all the variables

n^2-18n-63=0

a = 1; b = -18; c = -63;
Δ = b2-4ac
Δ = -182-4·1·(-63)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-24}{2*1}=\frac{-6}{2}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+24}{2*1}=\frac{42}{2}
=21
$