Slingshot Physics

I am investigating how the displacement of an elastic band affects the distance an attached object will travel (the relationship between how far back you pull a slingshot and the distance an object will travel). What I am trying to do is find a formula where distance travelled is a function of elastic band displacement (in other words, a formula which says "x = ... d..."), but I ended up very confused. I tried equation manipulation with the following equations:

W = F*d

W = ΔE_Kinetic

E_Kinetic = (1/2)*m*v²

and

E_{Elastic Potential} = (1/2)*k*x²

I got close to the final equation, but I couldn't make it. Here are a few things to keep in mind:

* In the final equation, where "x = ... d...", I don't want the force, F, to be in the equation.

* We are assuming that initial kinetic energy was 0 (meaning that the initial velocity was 0).

* We are assuming that the effects of friction and air resistance are negligible.

Thank you.