$$[\frac{9a-1}{3}]=\frac{3}{5}$$
$a=\frac{14}{45}\approx 0.311111111$
$$9a-1=\frac{3}{5}\times 3$$
$$9a-1=\frac{3\times 3}{5}$$
$$9a-1=\frac{9}{5}$$
$$9a=\frac{9}{5}+1$$
$$9a=\frac{9}{5}+\frac{5}{5}$$
$$9a=\frac{9+5}{5}$$
$$9a=\frac{14}{5}$$
$$a=\frac{\frac{14}{5}}{9}$$
$$a=\frac{14}{5\times 9}$$
$$a=\frac{14}{45}$$
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