Is it possible to to solve an equation with both power(?) and exponential terms for $x$?

Question

If I have an equation of the form $Y=A+x^B+C^x$ is it possible to solve for $x$, where $A$, $B$, and $C$ are all rational numbers?

More specifically, is it possible to solve $y=12 + 2x + x^{1.92} + 2^{0.425(x-12)}$ and, if so, how would I do it?

Answer 1

There is no nice formula that expresses $x$ as a function of $y$. For any particular numerical value of $y$ you can use software to find a value of $x$. For examples, if you ask Wolfram alpha to find $x$ when $y=100$

solve  12+2x+x^1.92+2^(0.425(x−12))=100

you find out that $y$ is

9.0984743836320913466

Since your function is increasing, it would be straightforward to write a python program (or a program in any other language) to find values by bisection, or to build a table of values as in a comment. You could even build a table of values in a spreadsheet.