2w(6w-1)=1

Solution for 2w(6w-1)=1 equation:

2w(6w-1)=1

We move all terms to the left:

2w(6w-1)-(1)=0

We multiply parentheses

12w^2-2w-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:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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