n^2+16n=-54

Solution for n^2+16n=-54 equation:

n^2+16n=-54

We move all terms to the left:

n^2+16n-(-54)=0

We add all the numbers together, and all the variables

n^2+16n+54=0

a = 1; b = 16; c = +54;
Δ = b2-4ac
Δ = 162-4·1·54
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{10}}{2*1}=\frac{-16-2\sqrt{10}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{10}}{2*1}=\frac{-16+2\sqrt{10}}{2}
$