Beispiel Nr: 14
$ \text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ x^2+3x-10 =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l} \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ 1x^{2}+3x-10 =0 \\ x_{1/2}=\displaystyle\frac{-3 \pm\sqrt{3^{2}-4\cdot 1 \cdot \left(-10\right)}}{2\cdot1} \\ x_{1/2}=\displaystyle \frac{-3 \pm\sqrt{49}}{2} \\ x_{1/2}=\displaystyle \frac{-3 \pm7}{2} \\ x_{1}=\displaystyle \frac{-3 +7}{2} \qquad x_{2}=\displaystyle \frac{-3 -7}{2} \\ x_{1}=2 \qquad x_{2}=-5 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ \\ x^{2}+3x-10 =0 \\ x_{1/2}=\displaystyle -\frac{3}{2}\pm\sqrt{\left(\frac{3}{2}\right)^2- \left(-10\right)} \\ x_{1/2}=\displaystyle -1\frac{1}{2}\pm\sqrt{12\frac{1}{4}} \\ x_{1/2}=\displaystyle -1\frac{1}{2}\pm3\frac{1}{2} \\ x_{1}=2 \qquad x_{2}=-5 \end{array}\\ \end{array}$