Beispiel Nr: 18
$ \text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ -\frac{1}{3}x^2-2x+3 =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l} \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ -\frac{1}{3}x^{2}-2x+3 =0 \\ x_{1/2}=\displaystyle\frac{+2 \pm\sqrt{\left(-2\right)^{2}-4\cdot \left(-\frac{1}{3}\right) \cdot 3}}{2\cdot\left(-\frac{1}{3}\right)} \\ x_{1/2}=\displaystyle \frac{+2 \pm\sqrt{8}}{-\frac{2}{3}} \\ x_{1/2}=\displaystyle \frac{2 \pm2,83}{-\frac{2}{3}} \\ x_{1}=\displaystyle \frac{2 +2,83}{-\frac{2}{3}} \qquad x_{2}=\displaystyle \frac{2 -2,83}{-\frac{2}{3}} \\ x_{1}=-7,24 \qquad x_{2}=1,24 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ -\frac{1}{3}x^{2}-2x+3 =0 \qquad /:-\frac{1}{3} \\ x^{2}+6x-9 =0 \\ x_{1/2}=\displaystyle -\frac{6}{2}\pm\sqrt{\left(\frac{6}{2}\right)^2- \left(-9\right)} \\ x_{1/2}=\displaystyle -3\pm\sqrt{18} \\ x_{1/2}=\displaystyle -3\pm4,24 \\ x_{1}=1,24 \qquad x_{2}=-7,24 \end{array}\\ \end{array}$