Take the square root of both sides of the equation.

$$(3x - 1)^2 = 12$$ $$\sqrt{(3x - 1)^2} = \pm\sqrt{12}$$ $$3x - 1 = \pm\sqrt{4 \times 3}$$ $$3x - 1 = \pm 2\sqrt{3}$$

Add 1 to both sides of the equation.

$$3x = 1 \pm 2\sqrt{3}$$

Divide both sides by 3.

$$x = \frac{1 \pm 2\sqrt{3}}{3}$$

The solutions for $x$ are $\boxed{\frac{1 + 2\sqrt{3}}{3}}$ and $\boxed{\frac{1 - 2\sqrt{3}}{3}}$.