The solutions to the equation $$\(x^{2}-\frac{3}{2 x}=\frac{24}{5}-2 x\)$$ are also the solutions to an equation of the form $$\(a x^{3}+b x^{2}+c x-15=0 \quad\)$$ where $$\(a, b\)$$ and $$\(c\)$$ are integers. Find the values of $$\(a, b\)$$ and $$\(c\)$$. $$\[ \begin{aligned} &a=......................... \\ &b=......................... \\ &c=......................... \end{aligned} \]$$

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