Answer
$x= \pm\frac{3}{2}i$
Work Step by Step
Solve for $x$:
$4x^{2}+9=0$
$4x^{2}=-9$
$x^{2}=-\displaystyle \frac{9}{4} $
$x=\displaystyle \pm\sqrt{-\frac{9}{4}}$
$=\displaystyle \pm\sqrt{(-1)\times \frac{9}{4}}$
As we know $\sqrt{-1}=i$, then
$=\pm\sqrt{\frac{9}{4}}i$
$=\pm\frac{3}{2}i$
Hence, $x= \pm\frac{3}{2}i$
