3x(2x-1)=6

Solution for 3x(2x-1)=6 equation:

3x(2x-1)=6

We move all terms to the left:

3x(2x-1)-(6)=0

We multiply parentheses

6x^2-3x-6=0

a = 6; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·6·(-6)
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{17}}{2*6}=\frac{3-3\sqrt{17}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{17}}{2*6}=\frac{3+3\sqrt{17}}{12}
$