$\begin{array}{l} \text{Gegeben:} ax^{3}+bx^{2}+cx+d=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ \\ \textbf{Gegeben:} \\ 1\frac{19}{35}x^3-10\frac{4}{5}x^2+18\frac{18}{35}x =0\\ \\ \textbf{Rechnung:} \\ x( 1\frac{19}{35}x^2-10\frac{4}{5}x+18\frac{18}{35})=0 \Rightarrow x=0 \quad \vee \quad 1\frac{19}{35}x^2-10\frac{4}{5}x+18\frac{18}{35}=0\\ \\ 1\frac{19}{35}x^{2}-10\frac{4}{5}x+18\frac{18}{35} =0 \\ x_{1/2}=\displaystyle\frac{+10\frac{4}{5} \pm\sqrt{\left(-10\frac{4}{5}\right)^{2}-4\cdot 1\frac{19}{35} \cdot 18\frac{18}{35}}}{2\cdot1\frac{19}{35}} \\ x_{1/2}=\displaystyle \frac{+10\frac{4}{5} \pm\sqrt{2,38}}{3\frac{3}{35}} \\ x_{1/2}=\displaystyle \frac{10\frac{4}{5} \pm1\frac{19}{35}}{3\frac{3}{35}} \\ x_{1}=\displaystyle \frac{10\frac{4}{5} +1\frac{19}{35}}{3\frac{3}{35}} \qquad x_{2}=\displaystyle \frac{10\frac{4}{5} -1\frac{19}{35}}{3\frac{3}{35}} \\ x_{1}=4 \qquad x_{2}=3 \\ \underline{x_1=0; \quad1\text{-fache Nullstelle}} \\\underline{x_2=3; \quad1\text{-fache Nullstelle}} \\\underline{x_3=4; \quad1\text{-fache Nullstelle}} \\ \end{array}$