Beispiel Nr: 23
$ \text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ -2x^2+3x+4 =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l} \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ -2x^{2}+3x+4 =0 \\ x_{1/2}=\displaystyle\frac{-3 \pm\sqrt{3^{2}-4\cdot \left(-2\right) \cdot 4}}{2\cdot\left(-2\right)} \\ x_{1/2}=\displaystyle \frac{-3 \pm\sqrt{41}}{-4} \\ x_{1/2}=\displaystyle \frac{-3 \pm6,4}{-4} \\ x_{1}=\displaystyle \frac{-3 +6,4}{-4} \qquad x_{2}=\displaystyle \frac{-3 -6,4}{-4} \\ x_{1}=-0,851 \qquad x_{2}=2,35 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ -2x^{2}+3x+4 =0 \qquad /:-2 \\ x^{2}-1\frac{1}{2}x-2 =0 \\ x_{1/2}=\displaystyle -\frac{-1\frac{1}{2}}{2}\pm\sqrt{\left(\frac{\left(-1\frac{1}{2}\right)}{2}\right)^2- \left(-2\right)} \\ x_{1/2}=\displaystyle \frac{3}{4}\pm\sqrt{2\frac{9}{16}} \\ x_{1/2}=\displaystyle \frac{3}{4}\pm1,6 \\ x_{1}=2,35 \qquad x_{2}=-0,851 \end{array}\\ \end{array}$