n^2+18n=-15

Solution for n^2+18n=-15 equation:

n^2+18n=-15

We move all terms to the left:

n^2+18n-(-15)=0

We add all the numbers together, and all the variables

n^2+18n+15=0

a = 1; b = 18; c = +15;
Δ = b2-4ac
Δ = 182-4·1·15
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{66}}{2*1}=\frac{-18-2\sqrt{66}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{66}}{2*1}=\frac{-18+2\sqrt{66}}{2}
$