0=12x^2+24x-96

Solution for 0=12x^2+24x-96 equation:

0=12x^2+24x-96

We move all terms to the left:

0-(12x^2+24x-96)=0

We add all the numbers together, and all the variables

-(12x^2+24x-96)=0

We get rid of parentheses

-12x^2-24x+96=0

a = -12; b = -24; c = +96;
Δ = b2-4ac
Δ = -242-4·(-12)·96
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-72}{2*-12}=\frac{-48}{-24}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+72}{2*-12}=\frac{96}{-24}
=-4
$