n^2+20n+72=-2

Solution for n^2+20n+72=-2 equation:

n^2+20n+72=-2

We move all terms to the left:

n^2+20n+72-(-2)=0

We add all the numbers together, and all the variables

n^2+20n+74=0

a = 1; b = 20; c = +74;
Δ = b2-4ac
Δ = 202-4·1·74
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{26}}{2*1}=\frac{-20-2\sqrt{26}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{26}}{2*1}=\frac{-20+2\sqrt{26}}{2}
$