Solve for S
S=\frac{a^{2}+b^{2}-c^{2}}{2}
Solve for a (complex solution)
a=-\sqrt{2S-b^{2}+c^{2}}
a=\sqrt{2S-b^{2}+c^{2}}
Solve for a
a=\sqrt{2S-b^{2}+c^{2}}
a=-\sqrt{2S-b^{2}+c^{2}}\text{, }S\geq \frac{b^{2}-c^{2}}{2}
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2S=a^{2}+b^{2}-c^{2}
Swap sides so that all variable terms are on the left hand side.
\frac{2S}{2}=\frac{a^{2}+b^{2}-c^{2}}{2}
Divide both sides by 2.
S=\frac{a^{2}+b^{2}-c^{2}}{2}
Dividing by 2 undoes the multiplication by 2.
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