n^2+18n+52=-4

Solution for n^2+18n+52=-4 equation:

n^2+18n+52=-4

We move all terms to the left:

n^2+18n+52-(-4)=0

We add all the numbers together, and all the variables

n^2+18n+56=0

a = 1; b = 18; c = +56;
Δ = b2-4ac
Δ = 182-4·1·56
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-10}{2*1}=\frac{-28}{2}
=-14
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+10}{2*1}=\frac{-8}{2}
=-4
$