y²-x=39;

The equation you've provided is

\[ y^2 - x = 39. \]

We can rearrange this equation to express \( x \) in terms of \( y \):

\[ y^2 - 39 = x \]

or

\[ x = y^2 - 39. \]

This equation describes a parabola that opens towards the right in the \( xy \)-plane. If you're looking for specific solutions, you can substitute different values of \( y \) into the equation to find corresponding \( x \) values.

If you would like to solve for specific values or need further analysis (like finding intersections, graphing, etc.), please let me know!