Question
$$5-4x-4x^2+x^3x = 3$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 5-4x-4x^2+x^3x &= 3&& \text{simplify left side} \\[1 em]5-4x-4x^2+x^4 &= 3&& \\[1 em]x^4-4x^2-4x+5 &= 3&& \text{move all terms to the left hand side } \\[1 em]x^4-4x^2-4x+5-3 &= 0&& \text{simplify left side} \\[1 em]x^4-4x^2-4x+2 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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Equations Solver