Is there a workaround. By the way I’m interested in exact solutions and not approximations, which in this case are t_1 = sqrt(5/3), t_2 = sqrt(1/2) (solved them with wolframalpha)

As for a Julia library Symbolics.jl’s solve_for only works for linear equations. I’m afraid for algebraic solves WolframAlpha is currently your best bet.

This is an area where WolframAlpha really shines and floor equations are unlikely to be a priority for most symbolic algebra packages. It might help if you explain why you need an exact solution and what generalizations of the equation are of interest (apparently you already know the answer to this one).

For this particular equation it is immediately obvious that any solution must be of the form t = sqrt((7n + 3) / 6) for some integer n and if it turns out that n <= t < n + 1 it is a valid solution. Then all that remains is to determine which integers n satisfy that relation.