$$2z^4-32z^3+204z^2-608z+714 = 0$$
Answer
$$ \begin{matrix}z_1 = 4+i & z_2 = 4-i & z_3 = 4+2.23607i \\[1 em] z_4 = 4-2.23607i & \\[1 em] \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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Polynomial Equations Solver