Question:
$x^{2}-2 x+\frac{3}{2}=0$
Solution:
$x^{2}-2 x+\frac{3}{2}=0$
$\Rightarrow x^{2}-2 x+1+\frac{1}{2}=0$
$\Rightarrow(x-1)^{2}-\left(\frac{1}{\sqrt{2}} i\right)^{2}=0$
$\Rightarrow\left(x-1+\frac{1}{\sqrt{2}} i\right)\left(x-1-\frac{1}{\sqrt{2}} i\right)=0$
$\Rightarrow\left(x-1-\frac{1}{\sqrt{2}} i\right)=0$ or, $\left(x-1+\frac{1}{\sqrt{2}} i\right)=0$
$\Rightarrow x=1+\frac{1}{\sqrt{2}} i \quad$ or, $\quad x=1-\frac{1}{\sqrt{2}} i$
Hence, the roots of the equation are $1 \pm \frac{1}{\sqrt{2}} i$.
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