Newton-Raphson method for the function

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So, I need to invert the following function

enter image description here and express alpha 2 in terms of D, where both t and alpha 1 are constant. Someone suggested the Newton-Raphson method, and here's what I've done so far

enter image description here enter image description here

Okay, but what do I do now? Any help would be appreciated. Sorry for the bad formatting.