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I did read on purple maths, that to understand the real method on solving a quadratic sequence, you have to understand calculus to a certain extent, unfortunally I have only just started reading calculus so I lack allot of knowledge in that specific area, which makes me think the formula was derived from a calculus equation; correct or not ?

I would really appreciate any insight into this formula, for example shown how it was derived, what the formula is called and if there is any text or web sites that I can be pointed to understand this more.

Thanks in advanced for any input; much appreciated.