0=12x^2-2x-1

Solution for 0=12x^2-2x-1 equation:

0=12x^2-2x-1

We move all terms to the left:

0-(12x^2-2x-1)=0

We add all the numbers together, and all the variables

-(12x^2-2x-1)=0

We get rid of parentheses

-12x^2+2x+1=0

a = -12; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-12)·1
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{13}}{2*-12}=\frac{-2-2\sqrt{13}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{13}}{2*-12}=\frac{-2+2\sqrt{13}}{-24}
$