$$-2500+x^2+\frac{101}{100}x^4+\frac{1}{400}x^6 = 0$$
Answer
$$ \begin{matrix}x_1 = 6.83111 & x_2 = -6.83111 & x_3 = 7.35044i \\[1 em] x_4 = -7.35044i & x_5 = 19.9157i & x_6 = -19.9157i \end{matrix} $$
Explanation
$$ \begin{aligned} -2500+x^2+\frac{101}{100}x^4+\frac{1}{400}x^6 &= 0&& \text{multiply ALL terms by } \color{blue}{ 400 }. \\[1 em]-400\cdot2500+400x^2+400 \cdot \frac{101}{100}x^4+400\frac{1}{400}x^6 &= 400\cdot0&& \text{cancel out the denominators} \\[1 em]-1000000+400x^2+404x^4+x^6 &= 0&& \text{simplify left side} \\[1 em]x^6+404x^4+400x^2-1000000 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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