27 The symbol $[x]$ represents the greatest integer not exceeding the real number $x$, then the solution to the equation $\left[3 x-4 \frac{5}{6}\right]-2 x-1=0$ is $\qquad$ .
276 or $6 \frac{1}{2} .2 x+1=\left[3 x-4 \frac{5}{6}\right]$ is an integer, so $x=k$ or $\frac{2 k+1}{2}$, where $k$ is an integer. When $x=k$,
$$
2 k+1=3 k-5, k=6, x=6
$$
When $x=\frac{2 k+1}{2}$
$$
2 k+2=3 k-4, k=6, x=6 \frac{1}{2} .
$$