Question:
$2 x^{2}-4 x+3=0$
Solution:
Given:
$2 x^{2}-4 x+3=0$
Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by:
$x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$
$\Rightarrow x=\frac{-(-4) \pm \sqrt{(-4)^{2}-(4 \times 2 \times 3)}}{2 \times 2}$
$\Rightarrow x=\frac{4 \pm \sqrt{16-24}}{4}$
$\Rightarrow x=\frac{4 \pm \sqrt{-8}}{4}$
$\Rightarrow x=\frac{4 \pm 2 \sqrt{2} i}{4}$
$\Rightarrow x=\frac{4}{4} \pm \frac{2 \sqrt{2}}{4} i$
$\Rightarrow \quad x=1 \pm \frac{i}{\sqrt{2}}$