Question

Solve
$2x^2-6x+3=0$

Answer 1

$2x^2-6x+3=0$

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

$\Rightarrow x^2-3x+\frac{3}{2}=0$

$\Rightarrow x^2-3x+\frac{3}{2}=0$

$\Rightarrow x^2-2\times \frac{3}{2}x+\frac{9}{4}-\frac{9}{4}+\frac{3}{2}=0$

$\Rightarrow {(x-\frac{3}{2})}^2=\frac{9}{4}-\frac{3}{2}$

$\Rightarrow {(x-\frac{3}{2})}^2=\frac{9-6}{4}$

$\Rightarrow {(x-\frac{3}{2})}^2=\frac{3}{4}$

$\Rightarrow x-\frac{3}{2}=\pm \frac{\sqrt{3}}{2}$

$\therefore x=\frac{3\pm \sqrt{3}}{2}$