There isn't a single "equation" for an elastic collision. Instead, the concept of an elastic collision is defined by a set of conservation laws:

Conservation of Momentum:

* Before the collision: m₁v₁ + m₂v₂ = Total momentum before

* After the collision: m₁v₁' + m₂v₂' = Total momentum after

* Equation: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'

Conservation of Kinetic Energy:

* Before the collision: (1/2)m₁v₁² + (1/2)m₂v₂² = Total kinetic energy before

* After the collision: (1/2)m₁v₁'² + (1/2)m₂v₂'² = Total kinetic energy after

* Equation: (1/2)m₁v₁² + (1/2)m₂v₂² = (1/2)m₁v₁'² + (1/2)m₂v₂'²

Where:

* m₁ and m₂ are the masses of the two objects.

* v₁ and v₂ are the initial velocities of the two objects.

* v₁' and v₂' are the final velocities of the two objects.

These two equations together define an elastic collision. They express the idea that in an elastic collision, the total momentum and the total kinetic energy of the system remain constant before and after the collision.

Note: These equations are for a simple scenario with two objects. For more complex scenarios, you would need to consider the vector nature of momentum and the total kinetic energy of all objects involved.