Question
$$7x^4-4x^2+5-\frac{3}{x^3} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 7x^4-4x^2+5-\frac{3}{x^3} &= 0&& \text{multiply ALL terms by } \color{blue}{ x^3 }. \\[1 em]x^3\cdot7x^4-x^3\cdot4x^2+x^3\cdot5-x^3\cdot\frac{3}{x^3} &= x^3\cdot0&& \text{cancel out the denominators} \\[1 em]7x^7-4x^5+5x^3-3 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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