Answer
$x=\displaystyle \pm i\frac{\sqrt{14}}{7}$
Work Step by Step
$ 7x^{2}-4=-6\qquad$ ...add $4$ to each side of the expression.
$ 7x^{2}=-2\qquad$ ...divide each term with $7$.
$ x^{2}=-\displaystyle \frac{2}{7}\qquad$ ...take square roots of each side.
$ x=\pm\sqrt{-\frac{2}{7}}\qquad$ ...write in terms of $i$.
$ x=\displaystyle \pm i\frac{\sqrt{2}}{\sqrt{7}}\qquad$ ...rationalize the radical by multiplying both the numerator and denominator with $\sqrt{7}$.
$\displaystyle \frac{\sqrt{2}}{\sqrt{7}}=\frac{\sqrt{2}\cdot\sqrt{7}}{\sqrt{7}\cdot\sqrt{7}}=\frac{\sqrt{14}}{7}$
$x=\displaystyle \pm i\frac{\sqrt{14}}{7}$
