Answer
$x=\frac{5}{8}$ or $x=\frac{2}{3}$.
Work Step by Step
By factorization, we have
$$24x^2 -31 x+10=(8x-5)(3x-2)=0.$$
Then we have
$$(8x-5)=0, \quad \text{or} \quad (3x-2) =0$$
that is $x=\frac{5}{8}$ or $x=\frac{2}{3}$.
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