w2+9w=-12

Solution for w2+9w=-12 equation:

w2+9w=-12

We move all terms to the left:

w2+9w-(-12)=0

We add all the numbers together, and all the variables

w^2+9w+12=0

a = 1; b = 9; c = +12;
Δ = b2-4ac
Δ = 92-4·1·12
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{33}}{2*1}=\frac{-9-\sqrt{33}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{33}}{2*1}=\frac{-9+\sqrt{33}}{2}
$