Solve for S
S=-\frac{3\left(2m-3\right)^{2}}{8}
Solve for m
m=-\frac{\sqrt{-6S}}{3}+\frac{3}{2}
m=\frac{\sqrt{-6S}}{3}+\frac{3}{2}\text{, }S\leq 0
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S=-\frac{3}{2}\left(m^{2}-3m+\frac{9}{4}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m-\frac{3}{2}\right)^{2}.
S=-\frac{3}{2}m^{2}+\frac{9}{2}m-\frac{27}{8}
Use the distributive property to multiply -\frac{3}{2} by m^{2}-3m+\frac{9}{4}.
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