That is certainly a messy equation when you try to rearrange for y. Personally I would change coordinates.
Changing to polar: , we get.
Maybe it's easier to work with from here.
I wanted to plot for C=840 but realised I couldn't isolate either x or y
I went to quickmath.com and entered the general equation and got...
Solve Equation :: QuickMath.com - Automatic Math Solutions
This returned 3 equations for calculating y; 2 complex and 1 real.
I know that for (7, 3), (7, 5) and (8, 7) are co-ordinates on the curve.
I cannot get these results by plugging in C=840, x=7 to the equations returned by quickmath.com.
Am I doing something wrong?