2n^2+9n+6=-3

Solution for 2n^2+9n+6=-3 equation:

2n^2+9n+6=-3

We move all terms to the left:

2n^2+9n+6-(-3)=0

We add all the numbers together, and all the variables

2n^2+9n+9=0

a = 2; b = 9; c = +9;
Δ = b2-4ac
Δ = 92-4·2·9
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3}{2*2}=\frac{-12}{4}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3}{2*2}=\frac{-6}{4}
=-1+1/2
$