n^2+18n+29=-8

Solution for n^2+18n+29=-8 equation:

n^2+18n+29=-8

We move all terms to the left:

n^2+18n+29-(-8)=0

We add all the numbers together, and all the variables

n^2+18n+37=0

a = 1; b = 18; c = +37;
Δ = b2-4ac
Δ = 182-4·1·37
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{11}}{2*1}=\frac{-18-4\sqrt{11}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{11}}{2*1}=\frac{-18+4\sqrt{11}}{2}
$