Question
$$2x^3-4x^2+8x-\frac{2}{x}+4 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 2x^3-4x^2+8x-\frac{2}{x}+4 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot2x^3-x\cdot4x^2+x\cdot8x-x\cdot\frac{2}{x}+x\cdot4 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]2x^4-4x^3+8x^2-2+4x &= 0&& \text{simplify left side} \\[1 em]2x^4-4x^3+8x^2+4x-2 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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Equations Solver