Solve for S
S=\frac{9+9m-3m^{2}}{2}
Solve for m
m=-\frac{\sqrt{189-24S}}{6}+\frac{3}{2}
m=\frac{\sqrt{189-24S}}{6}+\frac{3}{2}\text{, }S\leq \frac{63}{8}
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