.
There are infinitely many solutions.
For any integer n (positive, negative or zero) the number x = n + 0.2 is the solution.
There are NO other solutions.
For example, the numbers 0.2, 1.2, 5.2, -0.8, -12.8 are the solutions.
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Regarding the function floor(x), see this Wikipedia article
https://en.wikipedia.org/wiki/Floor_and_ceiling_functions
Its definition is THIS:
In mathematics, the floor function is the function that takes as input a real number x and gives as output the greatest integer
that is less than or equal to x.