8x(3x-1)=2

Solution for 8x(3x-1)=2 equation:

8x(3x-1)=2

We move all terms to the left:

8x(3x-1)-(2)=0

We multiply parentheses

24x^2-8x-2=0

a = 24; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·24·(-2)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*24}=\frac{-8}{48}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*24}=\frac{24}{48}
=1/2
$