$a=\frac{xy^{2}}{2}\text{ and }\frac{xy^{2}}{2}=3xy^{2}+5x-\frac{2y}{c}\text{ and }3xy^{2}+5x-\frac{2y}{c}=xy^{2}-3$

$x=\frac{6}{y^{2}}$
$y=\frac{\sqrt[3]{5}\left(\sqrt[3]{25c^{3}+2|c|\sqrt{150c^{2}+36}+12c}+\sqrt[3]{25c^{3}-2|c|\sqrt{150c^{2}+36}+12c}+5^{\frac{2}{3}}c\right)}{2}\text{ and }a=3\text{ and }c\neq 0$