Solve this

Given:

$3 x^{2}+7 i x+6=0$

$\Rightarrow 3 x^{2}+9 i x-2 i x+6=0$

$\Rightarrow 3 x(x+3 i)-2 i\left(x-\frac{6}{2 i}\right)=0$

$\Rightarrow \quad 3 x(x+3 i)-2 i\left(x-\frac{3 \times i}{i \times i}\right)=0 \quad \ldots\left(i^{2}=-1\right)$

$\Rightarrow 3 x(x+3 i)-2 i\left(x-\frac{3 \times i}{-1}\right)=0$

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

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

$\Rightarrow x+3 i=0 \& 3 x-2 i=0$

$\Rightarrow \mathrm{x}=3 \mathrm{i} \&^{x}=\frac{2}{3} i$

Ans: $\mathrm{x}=3 \mathrm{i}$ and $x=\frac{2}{3} i$