(3w^2)+11w=-6

Solution for (3w^2)+11w=-6 equation:

(3w^2)+11w=-6

We move all terms to the left:

(3w^2)+11w-(-6)=0

We add all the numbers together, and all the variables

3w^2+11w+6=0

a = 3; b = 11; c = +6;
Δ = b2-4ac
Δ = 112-4·3·6
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-7}{2*3}=\frac{-18}{6}
=-3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+7}{2*3}=\frac{-4}{6}
=-2/3
$