Beispiel Nr: 05
$ \text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ \frac{1}{4}x^2-3 =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l|l} \begin{array}{l} \text{Umformen}\\ \hline \frac{1}{4}x^2-3 =0 \qquad /+3 \\ \frac{1}{4}x^2= 3 \qquad /:\frac{1}{4} \\ x^2=\displaystyle\frac{3}{\frac{1}{4}} \\ x=\pm\sqrt{12} \\ x_1=3,46 \qquad x_2=-3,46 \end{array}& \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ \frac{1}{4}x^{2}+0x-3 =0 \\ x_{1/2}=\displaystyle\frac{-0 \pm\sqrt{0^{2}-4\cdot \frac{1}{4} \cdot \left(-3\right)}}{2\cdot\frac{1}{4}} \\ x_{1/2}=\displaystyle \frac{-0 \pm\sqrt{3}}{\frac{1}{2}} \\ x_{1/2}=\displaystyle \frac{0 \pm1,73}{\frac{1}{2}} \\ x_{1}=\displaystyle \frac{0 +1,73}{\frac{1}{2}} \qquad x_{2}=\displaystyle \frac{0 -1,73}{\frac{1}{2}} \\ x_{1}=3,46 \qquad x_{2}=-3,46 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ \frac{1}{4}x^{2}+0x-3 =0 \qquad /:\frac{1}{4} \\ x^{2}+0x-12 =0 \\ x_{1/2}=\displaystyle -\frac{0}{2}\pm\sqrt{\left(\frac{0}{2}\right)^2- \left(-12\right)} \\ x_{1/2}=\displaystyle 0\pm\sqrt{12} \\ x_{1/2}=\displaystyle 0\pm3,46 \\ x_{1}=3,46 \qquad x_{2}=-3,46 \end{array}\\ \end{array}$