x(6x-1)=6

Solution for x(6x-1)=6 equation:

x(6x-1)=6

We move all terms to the left:

x(6x-1)-(6)=0

We multiply parentheses

6x^2-1x-6=0

a = 6; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·6·(-6)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{145}}{2*6}=\frac{1-\sqrt{145}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{145}}{2*6}=\frac{1+\sqrt{145}}{12}
$