0=-12x^2-32x+384

Solution for 0=-12x^2-32x+384 equation:

0=-12x^2-32x+384

We move all terms to the left:

0-(-12x^2-32x+384)=0

We add all the numbers together, and all the variables

-(-12x^2-32x+384)=0

We get rid of parentheses

12x^2+32x-384=0

a = 12; b = 32; c = -384;
Δ = b2-4ac
Δ = 322-4·12·(-384)
Δ = 19456
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:

$\sqrt{\Delta}=\sqrt{19456}=\sqrt{1024*19}=\sqrt{1024}*\sqrt{19}=32\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32\sqrt{19}}{2*12}=\frac{-32-32\sqrt{19}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32\sqrt{19}}{2*12}=\frac{-32+32\sqrt{19}}{24}
$