n^2-20n-54=-10

Solution for n^2-20n-54=-10 equation:

n^2-20n-54=-10

We move all terms to the left:

n^2-20n-54-(-10)=0

We add all the numbers together, and all the variables

n^2-20n-44=0

a = 1; b = -20; c = -44;
Δ = b2-4ac
Δ = -202-4·1·(-44)
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{-(-20)-24}{2*1}=\frac{-4}{2}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+24}{2*1}=\frac{44}{2}
=22
$