e.g. Newton-Raphson , and the value of $x$ would need to be specified. With a table of values of $x$, $y(x)$ could be constructed by interpolation . Notice that if we consider the case $\alpha=-1/n$ for a natural number $n>2$, the equation is equivalent to $z^n-xz+1=0$ where $z=y^{1/n}$. share | improve