Réitigh x+a(2x+2m-4ex)[ln(x+m)-lnx]=0

$$x + a ( 2 x + 2 m - 4 e x ) [ \ln ( x + m ) - \ln x ] = 0$$

Réitigh do a. (complex solution)

$$a=-\frac{x}{2\left(m\ln(x+m)+x\ln(x+m)-m\ln(x)-x\ln(x)-2ex\ln(x+m)+2ex\ln(x)\right)}$$

$$-4ex\ln(x+m)+2m\ln(x+m)+2x\ln(x+m)+4ex\ln(x)-2m\ln(x)-2x\ln(x)\neq 0\text{ and }x\neq -m\text{ and }x\neq 0\text{ and }m\neq 0$$

Réitigh do a.

$$a=-\frac{x}{2\left(m\ln(x+m)+x\ln(x+m)-m\ln(x)-x\ln(x)-2ex\ln(x+m)+2ex\ln(x)\right)}$$

$$-4ex\ln(x+m)+2m\ln(x+m)+2x\ln(x+m)+4ex\ln(x)-2m\ln(x)-2x\ln(x)\neq 0\text{ and }x>-m\text{ and }x>0\text{ and }m\neq 0$$