Solve varepsilon:x=II:(x+tauI)

$$\varepsilon : x = I I : ( x + \tau I )$$

Solve for I (complex solution)

$$I=-\frac{\sqrt{\epsilon \left(x^{2}+\pi ^{2}\epsilon \right)}-\pi \epsilon }{x}$$

$$I=\frac{\sqrt{\epsilon \left(x^{2}+\pi ^{2}\epsilon \right)}+\pi \epsilon }{x}\text{, }x\neq 0$$

Solve for I

$$I=-\frac{\sqrt{\epsilon \left(x^{2}+\pi ^{2}\epsilon \right)}-\pi \epsilon }{x}$$

$$I=\frac{\sqrt{\epsilon \left(x^{2}+\pi ^{2}\epsilon \right)}+\pi \epsilon }{x}\text{, }x\neq 0\text{ and }\left(\epsilon \geq 0\text{ or }\epsilon \leq -\frac{x^{2}}{\pi ^{2}}\right)$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{2\pi I\epsilon }{\epsilon -I^{2}}\text{, }&I\neq 0\text{ and }\epsilon \neq 0\text{ and }\epsilon \neq I^{2}\\x\neq 0\text{, }&I=0\text{ and }\epsilon =0\end{matrix}\right.$$