0=-4x^2-24x-24

Solution for 0=-4x^2-24x-24 equation:

0=-4x^2-24x-24

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

4x^2+24x+24=0

a = 4; b = 24; c = +24;
Δ = b2-4ac
Δ = 242-4·4·24
Δ = 192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{3}}{2*4}=\frac{-24-8\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{3}}{2*4}=\frac{-24+8\sqrt{3}}{8}
$