9n^2+12n=-2

Solution for 9n^2+12n=-2 equation:

9n^2+12n=-2

We move all terms to the left:

9n^2+12n-(-2)=0

We add all the numbers together, and all the variables

9n^2+12n+2=0

a = 9; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·9·2
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{2}}{2*9}=\frac{-12-6\sqrt{2}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{2}}{2*9}=\frac{-12+6\sqrt{2}}{18}
$