0=12x^2-6x-4

Solution for 0=12x^2-6x-4 equation:

0=12x^2-6x-4

We move all terms to the left:

0-(12x^2-6x-4)=0

We add all the numbers together, and all the variables

-(12x^2-6x-4)=0

We get rid of parentheses

-12x^2+6x+4=0

a = -12; b = 6; c = +4;
Δ = b2-4ac
Δ = 62-4·(-12)·4
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{57}}{2*-12}=\frac{-6-2\sqrt{57}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{57}}{2*-12}=\frac{-6+2\sqrt{57}}{-24}
$