Help with physics equations in pool simulation

[Tsloasloa]

Hi, i was wondering if one of you lovely people would be able to help me.
Im wanting to code a pool simulation but thought i'd get the right equations first.

I don't need any help with the actual coding but I am confused at how i can use/implement the equations.

This: https://www.education.com/science-fair/article/linear-momentum-find-perfect-90/
website says in an elastic colision the difference in angles is always 90 degrees unluess the collision was head on. and it lists two equations, one for the velocitys of each ball after the collision(Ek), all good, and another for the x and y speeds after the collision (mv), but it generalises because the second ball was stationary at first. and I am unsure if I need to implement both of these or only one or what.

I also know I will need to implement a collision detecter which is trivial with circles but I will then need to timestep/move the balls back to the point of collision if the timestep is not small enough and am unsure of the best way to do this.

if anyone can help me with this, thanks x