Answer
$x=0\pm\dfrac{\sqrt{3}}{3}i$
Work Step by Step
$3x^{2}+1=0$
Take the $1$ to the right side:
$3x^{2}=-1$
Take the $3$ dividing to the right side of the equation:
$x^{2}=-\dfrac{1}{3}$
Take the square root of both sides:
$\sqrt{x^{2}}=\sqrt{-\dfrac{1}{3}}$
$x=\pm\sqrt{\dfrac{1}{3}}i=\pm\dfrac{1}{\sqrt{3}}i=\pm\dfrac{\sqrt{3}}{3}i$
The solution is $x=0\pm\dfrac{\sqrt{3}}{3}i$
