Beispiel Nr: 25
$\text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ -\frac{1}{3}x^2+2x+5 =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l} \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ -\frac{1}{3}x^{2}+2x+5 =0 \\ x_{1/2}=\displaystyle\frac{-2 \pm\sqrt{2^{2}-4\cdot \left(-\frac{1}{3}\right) \cdot 5}}{2\cdot\left(-\frac{1}{3}\right)} \\ x_{1/2}=\displaystyle \frac{-2 \pm\sqrt{10\frac{2}{3}}}{-\frac{2}{3}} \\ x_{1/2}=\displaystyle \frac{-2 \pm3,27}{-\frac{2}{3}} \\ x_{1}=\displaystyle \frac{-2 +3,27}{-\frac{2}{3}} \qquad x_{2}=\displaystyle \frac{-2 -3,27}{-\frac{2}{3}} \\ x_{1}=-1,9 \qquad x_{2}=7,9 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ -\frac{1}{3}x^{2}+2x+5 =0 \qquad /:-\frac{1}{3} \\ x^{2}-6x-15 =0 \\ x_{1/2}=\displaystyle -\frac{-6}{2}\pm\sqrt{\left(\frac{\left(-6\right)}{2}\right)^2- \left(-15\right)} \\ x_{1/2}=\displaystyle 3\pm\sqrt{24} \\ x_{1/2}=\displaystyle 3\pm4,9 \\ x_{1}=7,9 \qquad x_{2}=-1,9 \end{array}\\ \end{array}$