Let F be the Floor and f be the fractional part with  0 ≤ f < 1

(F+f) + 2f = 3F

3f = 2F

f = (2/3)F so F can only be 0 or 1

If F=0 then f=0.

If F=1 then f=2/3.

x can be {0 or 5/3}

5/3  + 2(2/3) = 3  checks

A computer check failed to pick up any solution other than zero until I checked for the difference being less than epsilon rather than requiring equality.

Output:

0.0

1e-05

2e-05

3e-05

1.66664

1.66665

1.66666

1.66667

1.66668

1.66669

-------------------

epsilon = .0001

import math

big = 500000

for i in range(-big,big):

    x = i/100000

    if abs(x+2*(x - math.floor(x)) - 3*math.floor(x)) < epsilon:

        print(x)