$\begin{array}{l} \text{Gegeben:} ax^{3}+bx^{2}+cx+d=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ \\ \textbf{Gegeben:} \\ \frac{1}{3}x^3-1x^2-1\frac{1}{3}x =0\\ \\ \textbf{Rechnung:} \\ x( \frac{1}{3}x^2-1x-1\frac{1}{3})=0 \Rightarrow x=0 \quad \vee \quad \frac{1}{3}x^2-1x-1\frac{1}{3}=0\\ \\ \frac{1}{3}x^{2}-1x-1\frac{1}{3} =0 \\ x_{1/2}=\displaystyle\frac{+1 \pm\sqrt{\left(-1\right)^{2}-4\cdot \frac{1}{3} \cdot \left(-1\frac{1}{3}\right)}}{2\cdot\frac{1}{3}} \\ x_{1/2}=\displaystyle \frac{+1 \pm\sqrt{2\frac{7}{9}}}{\frac{2}{3}} \\ x_{1/2}=\displaystyle \frac{1 \pm1\frac{2}{3}}{\frac{2}{3}} \\ x_{1}=\displaystyle \frac{1 +1\frac{2}{3}}{\frac{2}{3}} \qquad x_{2}=\displaystyle \frac{1 -1\frac{2}{3}}{\frac{2}{3}} \\ x_{1}=4 \qquad x_{2}=-1 \\ \underline{x_1=-1; \quad1\text{-fache Nullstelle}} \\\underline{x_2=0; \quad1\text{-fache Nullstelle}} \\\underline{x_3=4; \quad1\text{-fache Nullstelle}} \\ \end{array}$