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I checked this on a graphing calculator and noticed there are two solutions for this. How do I find them? Can they be found without the help of a calculator? They were some very arbitrary values, so this there some sort, patter (if that’s the right word to describe this), present in this?

Aditya
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    Have a look at this https://en.wikipedia.org/wiki/Dottie_number and this http://mathworld.wolfram.com/DottieNumber.html – Donald Splutterwit Dec 24 '19 at 13:02
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    A003957 – g.kov Dec 24 '19 at 13:03
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    Both sides of your equation are even functions of $x$, so the solutions are negatives of each other. There is no closed formula for the solution, but you can approximate it as well as you wish using iterations or Newton-Rhapson (faster). – Jyrki Lahtonen Dec 24 '19 at 13:05
  • You can find a very good precision of the solution but not exactly the solution. – dmtri Dec 24 '19 at 13:05
  • As I have found out, much to my dismay, I am treading on unfamiliar waters here. Honestly, this way beyond my current scope of studies, so I will pull back immediately. Thanks! – Aditya Dec 24 '19 at 13:15

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