Question
$$\frac{x^6}{216}+\frac{125}{216}-300\frac{x}{253} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{x^6}{216}+\frac{125}{216}-300\frac{x}{253} &= 0&& \text{multiply ALL terms by } \color{blue}{ 54648 }. \\[1 em]54648 \cdot \frac{x^6}{216}+54648\cdot\frac{125}{216}-54648\cdot300\frac{x}{253} &= 54648\cdot0&& \text{cancel out the denominators} \\[1 em]253x^6+31625-64800x &= 0&& \text{simplify left side} \\[1 em]253x^6-64800x+31625 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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