How to draw spheres on a curve with the same straight line distance between each other

As the title states, I am currently having trouble figuring out how to approach this problem. More specifically, I am currently using the using the equation y = mx^2 + ax. The problem is that if I increase x by a certain rate each frame, the spheres start to get spread out as the y starts growing way more rapidly. This makes the actual distance between the spheres different every time a draw a sphere. I have tried to potentially solve for x2 in the distance formula so i can find the new y, but this is proving to be pretty difficult for me. Can anyone point me in the direction of a solution for this? Sorry if this is a newb question, I am pretty new here and really just need some help!

A little more background information is that the spheres are not moving, so having them being spaced properly is a most, if not the curve looks dense at the beginning and super spaced out towards the end. If you need more background, please just post on what specifically you need and I would be glad to add it! Thanks!

 

This is only in 2d! Forgot to mention that. So no Z axis.

 

Still really need help!!!