Beispiel Nr: 06
$\text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ -2x^2+4 =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l|l} \begin{array}{l} \text{Umformen}\\ \hline -2x^2+4 =0 \qquad /-4 \\ -2x^2= -4 \qquad /:\left(-2\right) \\ x^2=\displaystyle\frac{-4}{-2} \\ x=\pm\sqrt{2} \\ x_1=1,41 \qquad x_2=-1,41 \end{array}& \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ -2x^{2}+0x+4 =0 \\ x_{1/2}=\displaystyle\frac{-0 \pm\sqrt{0^{2}-4\cdot \left(-2\right) \cdot 4}}{2\cdot\left(-2\right)} \\ x_{1/2}=\displaystyle \frac{-0 \pm\sqrt{32}}{-4} \\ x_{1/2}=\displaystyle \frac{0 \pm5,66}{-4} \\ x_{1}=\displaystyle \frac{0 +5,66}{-4} \qquad x_{2}=\displaystyle \frac{0 -5,66}{-4} \\ x_{1}=-1,41 \qquad x_{2}=1,41 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ -2x^{2}+0x+4 =0 \qquad /:-2 \\ x^{2}+0x-2 =0 \\ x_{1/2}=\displaystyle -\frac{0}{2}\pm\sqrt{\left(\frac{0}{2}\right)^2- \left(-2\right)} \\ x_{1/2}=\displaystyle 0\pm\sqrt{2} \\ x_{1/2}=\displaystyle 0\pm1,41 \\ x_{1}=1,41 \qquad x_{2}=-1,41 \end{array}\\ \end{array}$