Решите уравнение: (3x-x^2)/2+(2x^2-x)/6=x.

\[\frac{3x - x^{2}}{2} + \frac{2x^{2} - x}{6} = x\ \ \ \ | \cdot 6\]

\[3 \cdot \left( 3x - x^{2} \right) + 2x^{2} - x = 6x\]

\[9x - 3x^{2} + 2x^{2} - x = 6x\]

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

\[- x(x - 2) = 0\]

\[x = 0\ \ \ \ \ \ x - 2 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 2\]

\[Ответ:x = 0\ \ и\ \ x = 2.\]