Question
$$\frac{1}{2y^2}+\frac{1}{5y^1}-3 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{1}{2y^2}+\frac{1}{5y^1}-3 &= 0&& \text{multiply ALL terms by } \color{blue}{ 2y^2\cdot5y^1 }. \\[1 em]2y^2\cdot5y^1\cdot\frac{1}{2y^2}+2y^2\cdot5y^1\cdot\frac{1}{5y^1}-2y^2\cdot5y^1\cdot3 &= 2y^2\cdot5y^1\cdot0&& \text{cancel out the denominators} \\[1 em]5y+2-30y^3 &= 0&& \text{simplify left side} \\[1 em]-30y^3+5y+2 &= 0&& \\[1 em] \end{aligned} $$
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