The roots of polynomial $ p(d) $ are:
$$ \begin{aligned}d_1 &= \frac{ 8 }{ 5 }\\[1 em]d_2 &= \frac{ 2 }{ 3 } \end{aligned} $$The solutions of $ -15d^2+34d-16 = 0 $ are: $ d = \dfrac{ 2 }{ 3 } ~ \text{and} ~ d = \dfrac{ 8 }{ 5 }$.
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