0=-4x^2-16x+384

Solution for 0=-4x^2-16x+384 equation:

0=-4x^2-16x+384

We move all terms to the left:

0-(-4x^2-16x+384)=0

We add all the numbers together, and all the variables

-(-4x^2-16x+384)=0

We get rid of parentheses

4x^2+16x-384=0

a = 4; b = 16; c = -384;
Δ = b2-4ac
Δ = 162-4·4·(-384)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-80}{2*4}=\frac{-96}{8}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+80}{2*4}=\frac{64}{8}
=8
$