Question
$$4-5w^{2.5}w^2+2w-2.8-4w = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 4-5w^{2.5}w^2+2w-2.8-4w &= 0&& \text{simplify left side} \\[1 em]4-5\cdot1w^2w^2+2w-2.8-4w &= 0&& \\[1 em]4-5w^2w^2+2w-2.8-4w &= 0&& \\[1 em]4-5w^4+2w-2-4w &= 0&& \\[1 em]-5w^4-2w+2 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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Polynomial Equations Solver