12x^2-6x^-3=6

Solution for 12x^2-6x^-3=6 equation:

12x^2-6x^-3=6

We move all terms to the left:

12x^2-6x^-3-(6)=0

We add all the numbers together, and all the variables

12x^2-6x-9=0

a = 12; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·12·(-9)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{13}}{2*12}=\frac{6-6\sqrt{13}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{13}}{2*12}=\frac{6+6\sqrt{13}}{24}
$