Solve for G
G=\frac{x}{2}-\frac{1}{2x}
x\neq 0
Solve for x
x=-\sqrt{G^{2}+1}+G
x=\sqrt{G^{2}+1}+G
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2Gx=2x^{2}-1-x^{2}
Subtract x^{2} from both sides.
2Gx=x^{2}-1
Combine 2x^{2} and -x^{2} to get x^{2}.
2xG=x^{2}-1
The equation is in standard form.
\frac{2xG}{2x}=\frac{x^{2}-1}{2x}
Divide both sides by 2x.
G=\frac{x^{2}-1}{2x}
Dividing by 2x undoes the multiplication by 2x.
G=\frac{x}{2}-\frac{1}{2x}
Divide x^{2}-1 by 2x.
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