$\text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ -\frac{1}{2}x^2+4\frac{1}{2} =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l|l} \begin{array}{l} \text{Umformen}\\ \hline -\frac{1}{2}x^2+4\frac{1}{2} =0 \qquad /-4\frac{1}{2} \\ -\frac{1}{2}x^2= -4\frac{1}{2} \qquad /:\left(-\frac{1}{2}\right) \\ x^2=\displaystyle\frac{-4\frac{1}{2}}{-\frac{1}{2}} \\ x=\pm\sqrt{9} \\ x_1=3 \qquad x_2=-3 \end{array}& \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ -\frac{1}{2}x^{2}+0x+4\frac{1}{2} =0 \\ x_{1/2}=\displaystyle\frac{-0 \pm\sqrt{0^{2}-4\cdot \left(-\frac{1}{2}\right) \cdot 4\frac{1}{2}}}{2\cdot\left(-\frac{1}{2}\right)} \\ x_{1/2}=\displaystyle \frac{-0 \pm\sqrt{9}}{-1} \\ x_{1/2}=\displaystyle \frac{0 \pm3}{-1} \\ x_{1}=\displaystyle \frac{0 +3}{-1} \qquad x_{2}=\displaystyle \frac{0 -3}{-1} \\ x_{1}=-3 \qquad x_{2}=3 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ -\frac{1}{2}x^{2}+0x+4\frac{1}{2} =0 \qquad /:-\frac{1}{2} \\ x^{2}+0x-9 =0 \\ x_{1/2}=\displaystyle -\frac{0}{2}\pm\sqrt{\left(\frac{0}{2}\right)^2- \left(-9\right)} \\ x_{1/2}=\displaystyle 0\pm\sqrt{9} \\ x_{1/2}=\displaystyle 0\pm3 \\ x_{1}=3 \qquad x_{2}=-3 \end{array}\\ \end{array}$