Решите уравнение: 3x^4+5x^3-9x^2-9x+10=0.

\[3x^{4} + 5x^{3} - 9x^{2} - 9x + 10 = 0\]

\[x^{3}(3x + 5) - 9x^{2} - 9x - 6x + 6x + 10 = 0\]

\[x^{3}(3x + 5) - \left( 9x^{2} + 15x \right) + (6x + 10) = 0\]

\[x^{3}(3x + 5) - 3x(3x + 5) + 2(3x + 5) = 0\]

\[(3x + 5)\left( x^{2} - 3x + 2 \right) = 0\]

\[1)\ 3x + 5 = 0\]

\[3x = - 5\]

\[x = - \frac{5}{3} = - 1\frac{2}{3}.\]

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

\[x_{1} + x_{2} = 3;\ \ x_{1} \cdot x_{2} = 2\]

\[x_{1} = 1;\ \ x_{2} = 2.\]

\[Ответ:x = - 1\frac{2}{3};x = 1;x = 2.\]