\[ \bbox[#99CCFF,10px] {\Delta =b^{2}-4ac} \]

\[ \begin{align} & \Delta=\left(-{\frac{3}{2}}\right)^{2}-4.2.\frac{1}{4}\\ & \Delta=\frac{9}{4}-2=\frac{9-8}{4}\\ & \Delta =\frac{1}{4} \end{align} \]

\[ \bbox[#99CCFF,10px] {x_{1,2}=\frac{-b\pm \sqrt{\Delta \;}}{2a}} \]

\[ \begin{align} & x_{1,2}=\frac{-\left(-{\dfrac{3}{2}}\right)\pm\sqrt{\dfrac{1}{4}\;}}{2.2}\\[5pt] & x_{1,2}=\left(\frac{3}{2}\pm\frac{1}{2}\right).\frac{1}{4}\\[5pt] & x_{1}=\left(\frac{3}{2}+\frac{1}{2}\right).\frac{1}{4}=\frac{\cancel{4}}{2}.\frac{1}{\cancel{4}}=\frac{1}{2}\\[5pt] & x_{2}=\left(\frac{3}{2}-\frac{1}{2}\right).\frac{1}{4}=\frac{\cancel{2}}{\cancel{2}}.\frac{1}{4}=\frac{1}{4} \end{align} \]

\[ \bbox[#FFCCCC,10px] {V=\left\{\frac{1}{2},\frac{1}{4}\right\}} \]