Starting with an example function:

One first solves the equation for one x on the left from the original equation:

Then set y = 0 in this equation...

Then use this above formula and plug into a recursive structure like this:
Now you can plug in an initial guess (here -2):

And proceed recursively...

It approaches the root of 1.6666 quadratically...

**Proof**

Still working on a good proof...

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