n2-20n-22=-3

Solution for n2-20n-22=-3 equation:

n2-20n-22=-3

We move all terms to the left:

n2-20n-22-(-3)=0

We add all the numbers together, and all the variables

n^2-20n-19=0

a = 1; b = -20; c = -19;
Δ = b2-4ac
Δ = -202-4·1·(-19)
Δ = 476
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:

$\sqrt{\Delta}=\sqrt{476}=\sqrt{4*119}=\sqrt{4}*\sqrt{119}=2\sqrt{119}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{119}}{2*1}=\frac{20-2\sqrt{119}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{119}}{2*1}=\frac{20+2\sqrt{119}}{2}
$