0=6x^2+1x-1

Solution for 0=6x^2+1x-1 equation:

0=6x^2+1x-1

We move all terms to the left:

0-(6x^2+1x-1)=0

We add all the numbers together, and all the variables

-(6x^2+1x-1)=0

We get rid of parentheses

-6x^2-1x+1=0

a = -6; b = -1; c = +1;
Δ = b2-4ac
Δ = -12-4·(-6)·1
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*-6}=\frac{-4}{-12}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*-6}=\frac{6}{-12}
=-1/2
$