$$3x^6-6x^4+9x^3+2 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.55323 & x_2 = -1.88177 & x_3 = 0.21852+0.5896i \\[1 em] x_4 = 0.21852-0.5896i & x_5 = 0.99898+0.78845i & x_6 = 0.99898-0.78845i \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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