$$-3+12a^3-a^6 = 0$$
Answer
$$ \begin{matrix}a_1 = 0.63449 & a_2 = 2.27307 & a_3 = -0.31725+0.54949i \\[1 em] a_4 = -0.31725-0.54949i & a_5 = -1.13653+1.96853i & a_6 = -1.13653-1.96853i \end{matrix} $$
Explanation
$$ \begin{aligned} -3+12a^3-a^6 &= 0&& \text{simplify left side} \\[1 em]-a^6+12a^3-3 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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