Beispiel Nr: 40
$ \text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ \frac{3}{49}x^2-\frac{6}{49}x-2\frac{46}{49} =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l} \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ \frac{3}{49}x^{2}-\frac{6}{49}x-2\frac{46}{49} =0 \\ x_{1/2}=\displaystyle\frac{+\frac{6}{49} \pm\sqrt{\left(-\frac{6}{49}\right)^{2}-4\cdot \frac{3}{49} \cdot \left(-2\frac{46}{49}\right)}}{2\cdot\frac{3}{49}} \\ x_{1/2}=\displaystyle \frac{+\frac{6}{49} \pm\sqrt{\frac{36}{49}}}{\frac{6}{49}} \\ x_{1/2}=\displaystyle \frac{\frac{6}{49} \pm\frac{6}{7}}{\frac{6}{49}} \\ x_{1}=\displaystyle \frac{\frac{6}{49} +\frac{6}{7}}{\frac{6}{49}} \qquad x_{2}=\displaystyle \frac{\frac{6}{49} -\frac{6}{7}}{\frac{6}{49}} \\ x_{1}=8 \qquad x_{2}=-6 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ \frac{3}{49}x^{2}-\frac{6}{49}x-2\frac{46}{49} =0 \qquad /:\frac{3}{49} \\ x^{2}-2x-48 =0 \\ x_{1/2}=\displaystyle -\frac{-2}{2}\pm\sqrt{\left(\frac{\left(-2\right)}{2}\right)^2- \left(-48\right)} \\ x_{1/2}=\displaystyle 1\pm\sqrt{49} \\ x_{1/2}=\displaystyle 1\pm7 \\ x_{1}=8 \qquad x_{2}=-6 \end{array}\\ \end{array}$