-6q^2-4q=-32

Solution for -6q^2-4q=-32 equation:

-6q^2-4q=-32

We move all terms to the left:

-6q^2-4q-(-32)=0

We add all the numbers together, and all the variables

-6q^2-4q+32=0

a = -6; b = -4; c = +32;
Δ = b2-4ac
Δ = -42-4·(-6)·32
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-28}{2*-6}=\frac{-24}{-12}
=+2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+28}{2*-6}=\frac{32}{-12}
=-2+2/3
$