0=12x^2+x-1

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

0=12x^2+x-1

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-12x^2-x+1=0

We add all the numbers together, and all the variables

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

a = -12; b = -1; c = +1;
Δ = b2-4ac
Δ = -12-4·(-12)·1
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7}{2*-12}=\frac{-6}{-24}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*-12}=\frac{8}{-24}
=-1/3
$