How to solve an equation involving the floor of a number? I'm looking for a solving procedure for this type of exercises.

If $[x]$ represents the floor of $x$, solve the equation:
$$\left[\frac{6x+5}8\right]=\frac{15x-7}5$$
Choose the correct answer:
a) {$\frac{4}5$}
b) {$\frac{3}4$}
c) {$\frac{7}{15}$,$\frac{4}5$} 
d) {$\frac{6}{15}$} 
e) {$\frac{1}{2}$,$\frac{3}4$} 
f) {$\frac{1}{2}$,$\frac{4}5$} 

Can someone please explain how I can solve this equation? Thank you very much!
ps. I asked a similar question, unfortunately, the same method doesn't seem to work.

Let $\mathbb{Z} \ni k = \lfloor \frac{6 x+ 5}{8} \rfloor$. Then the equation says $x = \frac{k}{3} + \frac{7}{15}$. Now we write the equation for $k$:
$$
    k = \left\lfloor \frac{k}{4} + \frac{39}{40} \right\rfloor
$$
It now remains to test few small values of $k$. Values $k=0$ and $k=1$ work out. 

These correspond to $x = \frac{7}{15}$ and $x=\frac{12}{15} = \frac{4}{5}$.
