This is cheating...but have a look at the graph of y = floor(x) and y = 2x + 3...seen here....https://www.desmos.com/calculator/8kenredv3g
Notice that there appear to be only two points of interesection in the two graphs.... one at (-3, -3) and one at (-3.5, -4)
There is also another "near" miss at (-4, -5).....but 2(-4) + 3 = -5 ....but floor (-4) = -4 ...so they do not intersect when x = -4....
So the x (or, t, if you prefer) values that make this true is when t = -3 and t = -3.5
Note the oddity here.....if the graphs were both just "linear," and because they have different "slopes," there would be- at most - only one point of intersection, ....but since the "floor" function isn't truly a linear function, it actually gives rise to an additional intersection point...!!!
I don't think a graphical solution is "cheating" - it seems perfectly valid to me. However, if you want a non-graphical method then here is a possibility:
(That last d should be a δ, of course!)