Find the roots of the equation $2{\mathrm{x}}^2-7\mathrm{x}+3=0$ using the method of completion of the square.

Given equation:  $2{\mathrm{x}}^2-7\mathrm{x}+3=0$

${\mathrm{x}}^2-\frac{7}{2}\mathrm{x}+\frac{3}{2}=0$

${\mathrm{x}}^2-2\times \mathrm{x}\times \frac{7}{4}+\frac{3}{2}=0$

${\mathrm{x}}^2-2\times \mathrm{x}\times \frac{7}{4}+{\left(\frac{7}{4}\right)}^2-{\left(\frac{7}{4}\right)}^2+\frac{3}{2}=0$

${\left(\mathrm{x}-\frac{7}{4}\right)}^2-\frac{49}{16}+\frac{3}{2}=0$

$\mathrm{x}-\frac{7}{4}=\pm \frac{5}{4}$

$\mathrm{x}=\frac{7}{4}\pm \frac{5}{4}=3,\frac{1}{2}$