0=12x^2-1160x-384

Solution for 0=12x^2-1160x-384 equation:

0=12x^2-1160x-384

We move all terms to the left:

0-(12x^2-1160x-384)=0

We add all the numbers together, and all the variables

-(12x^2-1160x-384)=0

We get rid of parentheses

-12x^2+1160x+384=0

a = -12; b = 1160; c = +384;
Δ = b2-4ac
Δ = 11602-4·(-12)·384
Δ = 1364032
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:

$\sqrt{\Delta}=\sqrt{1364032}=\sqrt{64*21313}=\sqrt{64}*\sqrt{21313}=8\sqrt{21313}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1160)-8\sqrt{21313}}{2*-12}=\frac{-1160-8\sqrt{21313}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1160)+8\sqrt{21313}}{2*-12}=\frac{-1160+8\sqrt{21313}}{-24}
$