Beispiel Nr: 42
$ \text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ -1\frac{1}{4}x^2-10x-15 =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l} \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ -1\frac{1}{4}x^{2}-10x-15 =0 \\ x_{1/2}=\displaystyle\frac{+10 \pm\sqrt{\left(-10\right)^{2}-4\cdot \left(-1\frac{1}{4}\right) \cdot \left(-15\right)}}{2\cdot\left(-1\frac{1}{4}\right)} \\ x_{1/2}=\displaystyle \frac{+10 \pm\sqrt{25}}{-2\frac{1}{2}} \\ x_{1/2}=\displaystyle \frac{10 \pm5}{-2\frac{1}{2}} \\ x_{1}=\displaystyle \frac{10 +5}{-2\frac{1}{2}} \qquad x_{2}=\displaystyle \frac{10 -5}{-2\frac{1}{2}} \\ x_{1}=-6 \qquad x_{2}=-2 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ -1\frac{1}{4}x^{2}-10x-15 =0 \qquad /:-1\frac{1}{4} \\ x^{2}+8x+12 =0 \\ x_{1/2}=\displaystyle -\frac{8}{2}\pm\sqrt{\left(\frac{8}{2}\right)^2- 12} \\ x_{1/2}=\displaystyle -4\pm\sqrt{4} \\ x_{1/2}=\displaystyle -4\pm2 \\ x_{1}=-2 \qquad x_{2}=-6 \end{array}\\ \end{array}$