-2q^2-4q=-24

Solution for -2q^2-4q=-24 equation:

-2q^2-4q=-24

We move all terms to the left:

-2q^2-4q-(-24)=0

We add all the numbers together, and all the variables

-2q^2-4q+24=0

a = -2; b = -4; c = +24;
Δ = b2-4ac
Δ = -42-4·(-2)·24
Δ = 208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{13}}{2*-2}=\frac{4-4\sqrt{13}}{-4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{13}}{2*-2}=\frac{4+4\sqrt{13}}{-4}
$