Solve for x_0
x_{0}=\frac{3x}{2}+\frac{1}{2x}
x\neq 0
Solve for x (complex solution)
x=\frac{\sqrt{x_{0}^{2}-3}+x_{0}}{3}
x=\frac{-\sqrt{x_{0}^{2}-3}+x_{0}}{3}
Solve for x
x=\frac{\sqrt{x_{0}^{2}-3}+x_{0}}{3}
x=\frac{-\sqrt{x_{0}^{2}-3}+x_{0}}{3}\text{, }|x_{0}|\geq \sqrt{3}
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-2xx_{0}=-1-3x^{2}
Subtract 3x^{2} from both sides.
\left(-2x\right)x_{0}=-3x^{2}-1
The equation is in standard form.
\frac{\left(-2x\right)x_{0}}{-2x}=\frac{-3x^{2}-1}{-2x}
Divide both sides by -2x.
x_{0}=\frac{-3x^{2}-1}{-2x}
Dividing by -2x undoes the multiplication by -2x.
x_{0}=\frac{3x}{2}+\frac{1}{2x}
Divide -1-3x^{2} by -2x.
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