Question
$$7480x\cdot\frac{2}{3}x\cdot\frac{3}{4}+\frac{5}{x} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 7480x\cdot\frac{2}{3}x\cdot\frac{3}{4}+\frac{5}{x} &= 0&& \text{multiply ALL terms by } \color{blue}{ 3\cdot4x }. \\[1 em]3\cdot4x7480x\cdot\frac{2}{3}x\cdot\frac{3}{4}+3\cdot4x\cdot\frac{5}{x} &= 3\cdot4x\cdot0&& \text{cancel out the denominators} \\[1 em]44880x^3+60 &= 0&& \\[1 em] \end{aligned} $$
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