Question
$$10x^2+17x-\frac{6}{x}-4 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 10x^2+17x-\frac{6}{x}-4 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot10x^2+x\cdot17x-x\cdot\frac{6}{x}-x\cdot4 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]10x^3+17x^2-6-4x &= 0&& \text{simplify left side} \\[1 em]10x^3+17x^2-4x-6 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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Equations Solver