252. $\frac{x}{10-x}+\frac{10-x}{x}=25$.
252. $10 x=x^{2}+\frac{100}{27} ; x=5-\sqrt{21 \frac{8}{27}}$. But Regiomontanus also gives another solution, assuming $\frac{x}{10-x}=y$. Then $y+\frac{1}{y}=25 ; y=\frac{25}{2}-\sqrt{\frac{621}{4}}$. In both cases, Regiomontanus takes the roots with a minus sign.