Answer
$x=\frac{1}{2}$ or $x=8$.
Work Step by Step
By factorization, we have
$$2x^2-17 x-8=(2x-1)(x-8)=0.$$
Then we have
$$(2x-1) =0, \quad \text{or} \quad )(x-8)=0$$
that is $x=\frac{1}{2}$ or $x=8$.
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