q^2+9q=-6

Solution for q^2+9q=-6 equation:

q^2+9q=-6

We move all terms to the left:

q^2+9q-(-6)=0

We add all the numbers together, and all the variables

q^2+9q+6=0

a = 1; b = 9; c = +6;
Δ = b2-4ac
Δ = 92-4·1·6
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{57}}{2*1}=\frac{-9-\sqrt{57}}{2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{57}}{2*1}=\frac{-9+\sqrt{57}}{2}
$