n^2+18n=-75

Solution for n^2+18n=-75 equation:

n^2+18n=-75

We move all terms to the left:

n^2+18n-(-75)=0

We add all the numbers together, and all the variables

n^2+18n+75=0

a = 1; b = 18; c = +75;
Δ = b2-4ac
Δ = 182-4·1·75
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{6}}{2*1}=\frac{-18-2\sqrt{6}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{6}}{2*1}=\frac{-18+2\sqrt{6}}{2}
$