Solve for g
g=\frac{x}{2}-2-\frac{1}{x}
x\neq 0
Solve for x
x=-\sqrt{g^{2}+4g+6}+g+2
x=\sqrt{g^{2}+4g+6}+g+2
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4gx=2x^{2}-7x-4-x
Subtract x from both sides.
4gx=2x^{2}-8x-4
Combine -7x and -x to get -8x.
4xg=2x^{2}-8x-4
The equation is in standard form.
\frac{4xg}{4x}=\frac{2x^{2}-8x-4}{4x}
Divide both sides by 4x.
g=\frac{2x^{2}-8x-4}{4x}
Dividing by 4x undoes the multiplication by 4x.
g=\frac{x}{2}-2-\frac{1}{x}
Divide -8x-4+2x^{2} by 4x.
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Limits
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