Solve the following

Given: $9 x^{2}+4=0$

$9 x^{2}+4=0$

$\Rightarrow(3 x)^{2}+2^{2}=0$

$\Rightarrow(3 x)^{2}-(2 i)^{2}=0$

$\Rightarrow(3 x+2 i)(3 x-2 i)=0 \quad\left[\left(a^{2}-b^{2}\right)=(a+b)(a-b)\right]$

$\Rightarrow(3 x+2 i)=0$ or, $(3 x-2 i)=0$

$\Rightarrow 3 x=-2 i$ or $3 x=2 i$

$\Rightarrow x=-\frac{2 i}{3}$ or $x=\frac{2 i}{3}$

Hence, the roots of the equation are $\frac{2 i}{3}$ and $-\frac{2 i}{3}$.