Решите уравнение: 9x^3-18x^2=x-2.

\[9x^{3} - 18x^{2} = x - 2\]

\[9x^{3} - 18x^{2} - x + 2 = 0\]

\[9x^{2}(x - 2) - (x - 2) = 0\]

\[(x - 2)\left( 9x^{2} - 1 \right) = 0\]

\[x - 2 = 0\]

\[x = 2.\]

\[9x^{2} - 1 = 0\]

\[9x^{2} = 1\]

\[x^{2} = \frac{1}{9}\]

\[x = \pm \frac{1}{3}.\]

\[Ответ:x = \pm \frac{1}{3};x = 2.\]