$$y^6-1686y^5-525624y^4+71116y^3+36y^2-20-6 = 0$$
Answer
$$ \begin{matrix}y_1 = -268.99702 & y_2 = 1954.86178 & y_3 = -0.03793+0.0527i \\[1 em] y_4 = -0.03793-0.0527i & y_5 = 0.10555+0.02426i & y_6 = 0.10555-0.02426i \end{matrix} $$
Explanation
$$ \begin{aligned} y^6-1686y^5-525624y^4+71116y^3+36y^2-20-6 &= 0&& \text{simplify left side} \\[1 em]y^6-1686y^5-525624y^4+71116y^3+36y^2-26 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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