Beispiel Nr: 32
$ \text{Gegeben:} ax^{3}+bx^{2}+cx+d=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ \\ \textbf{Gegeben:} \\ 5\frac{2}{5}x^3+27x^2+32\frac{2}{5}x =0\\ \\ \textbf{Rechnung:} \\ x( 5\frac{2}{5}x^2+27x+32\frac{2}{5})=0 \Rightarrow x=0 \quad \vee \quad 5\frac{2}{5}x^2+27x+32\frac{2}{5}=0\\ \\ 5\frac{2}{5}x^{2}+27x+32\frac{2}{5} =0 \\ x_{1/2}=\displaystyle\frac{-27 \pm\sqrt{27^{2}-4\cdot 5\frac{2}{5} \cdot 32\frac{2}{5}}}{2\cdot5\frac{2}{5}} \\ x_{1/2}=\displaystyle \frac{-27 \pm\sqrt{29\frac{4}{25}}}{10\frac{4}{5}} \\ x_{1/2}=\displaystyle \frac{-27 \pm5\frac{2}{5}}{10\frac{4}{5}} \\ x_{1}=\displaystyle \frac{-27 +5\frac{2}{5}}{10\frac{4}{5}} \qquad x_{2}=\displaystyle \frac{-27 -5\frac{2}{5}}{10\frac{4}{5}} \\ x_{1}=-2 \qquad x_{2}=-3 \\ \underline{x_1=-3; \quad1\text{-fache Nullstelle}} \\\underline{x_2=-2; \quad1\text{-fache Nullstelle}} \\\underline{x_3=0; \quad1\text{-fache Nullstelle}} \\$