Solve for x_0
x_{0}=2x-\frac{1}{x}
x\neq 0
Solve for x
x=\frac{\sqrt{x_{0}^{2}+8}+x_{0}}{4}
x=\frac{-\sqrt{x_{0}^{2}+8}+x_{0}}{4}
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-2xx_{0}=2-4x^{2}
Subtract 4x^{2} from both sides.
\left(-2x\right)x_{0}=2-4x^{2}
The equation is in standard form.
\frac{\left(-2x\right)x_{0}}{-2x}=\frac{2-4x^{2}}{-2x}
Divide both sides by -2x.
x_{0}=\frac{2-4x^{2}}{-2x}
Dividing by -2x undoes the multiplication by -2x.
x_{0}=2x-\frac{1}{x}
Divide 2-4x^{2} by -2x.
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