Question:
$2 x^{2}+3 i x+2=0$
Solution:
Given
$2 x^{2}+3 i x+2=0$
$\Rightarrow 2 x^{2}+4 i x-i x+2=0$
$\Rightarrow 2 x(x+2 i)-i\left(x-\frac{2}{i}\right)=0$
$\Rightarrow 2 x(x+2 i)-i\left(x-\frac{2 \times i}{i \times i}\right)=0$
$\Rightarrow 2 x(x+2 i)-i\left(x-\frac{2 \times i}{-1}\right)=0$
$\Rightarrow 2 x(x+2 i)-i(x+2 i)=0$
$\Rightarrow(x+2 i)(2 x-i)=0$
$\Rightarrow x+2 i=0 \& 2 x-i=0$
$\Rightarrow \mathrm{x}=-2 \mathrm{i} \&^{x=\frac{i}{2}}$
Ans: $\mathrm{x}=-2 \mathrm{i}$ and $^{x}=\frac{i}{2}$
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