$$3x^4+26x^3+77x^2+84x+24 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.43492 & x_2 = -1.60972 & x_3 = -3.31101+0.68124i \\[1 em] x_4 = -3.31101-0.68124i & \\[1 em] \end{matrix} $$
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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Polynomial Equations Solver