$$-3x-9x+7x^4+6 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.55558 & x_2 = 0.92255 & x_3 = -0.73906+1.06118i \\[1 em] x_4 = -0.73906-1.06118i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} -3x-9x+7x^4+6 &= 0&& \text{simplify left side} \\[1 em]7x^4-12x+6 &= 0&& \\[1 em] \end{aligned} $$
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