Question
$$10000 = \frac{3384}{100}x^5-\frac{5478}{10}x^4+\frac{33712}{10}x^3-\frac{90285}{10}x^2+\frac{101220}{10}x+\frac{4889}{100}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 10000 &= \frac{3384}{100}x^5-\frac{5478}{10}x^4+\frac{33712}{10}x^3-\frac{90285}{10}x^2+\frac{101220}{10}x+\frac{4889}{100}&& \text{multiply ALL terms by } \color{blue}{ 100 }. \\[1 em]100\cdot10000 &= 100 \cdot \frac{3384}{100}x^5-100\frac{5478}{10}x^4+100\frac{33712}{10}x^3-100\frac{90285}{10}x^2+100\frac{101220}{10}x+100\cdot\frac{4889}{100}&& \text{cancel out the denominators} \\[1 em]1000000 &= 3384x^5-54780x^4+337120x^3-902850x^2+1012200x+4889&& \text{move all terms to the left hand side } \\[1 em]1000000-3384x^5+54780x^4-337120x^3+902850x^2-1012200x-4889 &= 0&& \text{simplify left side} \\[1 em]-3384x^5+54780x^4-337120x^3+902850x^2-1012200x+995111 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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