$$\frac{3-x}{x} = \frac{x+1}{2x}$$
Answer
$$ \begin{matrix}x_1 = 1.2483 & x_2 = -1.12415+1.88224i & x_3 = -1.12415-1.88224i \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{3-x}{x} &= \frac{x+1}{2x}&& \text{multiply ALL terms by } \color{blue}{ x\cdot2 }. \\[1 em]x\cdot2 \cdot \frac{3-x}{x} &= x\cdot2 \cdot \frac{x+1}{2x}&& \text{cancel out the denominators} \\[1 em]-2x+6 &= x^3+x^2&& \text{move all terms to the left hand side } \\[1 em]-2x+6-x^3-x^2 &= 0&& \text{simplify left side} \\[1 em]-x^3-x^2-2x+6 &= 0&& \\[1 em] \end{aligned} $$
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