#### Answer

$ x = (\frac{1+2i}{3}, \frac{1-2i}{3})$

#### Work Step by Step

$(3x-1)^2 = -4$
$3x-1 = ±\sqrt -4$ (Use Square root Property)
$3x-1= ± 2i$ (Simplify the radical)
$3x = 1 ± 2i$ (Add 1 to both sides)
$x=\frac{1±2i}{3}$ (Divide by 3 on both sides)
The solution set is $(\frac{1 + 2i}{3}, \frac{1-2i}{3})$
Note : Root of a negative number is a complex number and is represented by 'i'