n^2+18n+73=0

Solution for n^2+18n+73=0 equation:

n^2+18n+73=0

a = 1; b = 18; c = +73;
Δ = b2-4ac
Δ = 182-4·1·73
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{2}}{2*1}=\frac{-18-4\sqrt{2}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{2}}{2*1}=\frac{-18+4\sqrt{2}}{2}
$