$$r^4+7r^3+3r^2-8r-4 = 0$$
Answer
$$ \begin{matrix}r_1 = -0.5101 & r_2 = -1.18713 & r_3 = 1.04123 \\[1 em] r_4 = -6.344 & \\[1 em] \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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