Beispiel Nr: 44
$ \text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ -\frac{24}{49}x^2+2\frac{22}{49}x+2\frac{46}{49} =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l} \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ -\frac{24}{49}x^{2}+2\frac{22}{49}x+2\frac{46}{49} =0 \\ x_{1/2}=\displaystyle\frac{-2\frac{22}{49} \pm\sqrt{\left(2\frac{22}{49}\right)^{2}-4\cdot \left(-\frac{24}{49}\right) \cdot 2\frac{46}{49}}}{2\cdot\left(-\frac{24}{49}\right)} \\ x_{1/2}=\displaystyle \frac{-2\frac{22}{49} \pm\sqrt{11\frac{37}{49}}}{-\frac{48}{49}} \\ x_{1/2}=\displaystyle \frac{-2\frac{22}{49} \pm3\frac{3}{7}}{-\frac{48}{49}} \\ x_{1}=\displaystyle \frac{-2\frac{22}{49} +3\frac{3}{7}}{-\frac{48}{49}} \qquad x_{2}=\displaystyle \frac{-2\frac{22}{49} -3\frac{3}{7}}{-\frac{48}{49}} \\ x_{1}=-1 \qquad x_{2}=6 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ -\frac{24}{49}x^{2}+2\frac{22}{49}x+2\frac{46}{49} =0 \qquad /:-\frac{24}{49} \\ x^{2}-5x-6 =0 \\ x_{1/2}=\displaystyle -\frac{-5}{2}\pm\sqrt{\left(\frac{\left(-5\right)}{2}\right)^2- \left(-6\right)} \\ x_{1/2}=\displaystyle 2\frac{1}{2}\pm\sqrt{12\frac{1}{4}} \\ x_{1/2}=\displaystyle 2\frac{1}{2}\pm3\frac{1}{2} \\ x_{1}=6 \qquad x_{2}=-1 \end{array}\\ \end{array}$