Beispiel Nr: 07
$ \text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ x^2-2 =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l|l} \begin{array}{l} \text{Umformen}\\ \hline 1x^2-2 =0 \qquad /+2 \\ 1x^2= 2 \qquad /:1 \\ x^2=\displaystyle\frac{2}{1} \\ x=\pm\sqrt{2} \\ x_1=1,41 \qquad x_2=-1,41 \end{array}& \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ 1x^{2}+0x-2 =0 \\ x_{1/2}=\displaystyle\frac{-0 \pm\sqrt{0^{2}-4\cdot 1 \cdot \left(-2\right)}}{2\cdot1} \\ x_{1/2}=\displaystyle \frac{-0 \pm\sqrt{8}}{2} \\ x_{1/2}=\displaystyle \frac{0 \pm2,83}{2} \\ x_{1}=\displaystyle \frac{0 +2,83}{2} \qquad x_{2}=\displaystyle \frac{0 -2,83}{2} \\ x_{1}=1,41 \qquad x_{2}=-1,41 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ \\ x^{2}+0x-2 =0 \\ x_{1/2}=\displaystyle -\frac{0}{2}\pm\sqrt{\left(\frac{0}{2}\right)^2- \left(-2\right)} \\ x_{1/2}=\displaystyle 0\pm\sqrt{2} \\ x_{1/2}=\displaystyle 0\pm1,41 \\ x_{1}=1,41 \qquad x_{2}=-1,41 \end{array}\\ \end{array}$