I'm trying to solve the equation
$24.6347 \left(246.347 x + \sqrt{(246.347 x + 20)^2 + 1} + 20\right)^{-a} =\\ 30.2879 \left(-33.6532 x + \sqrt{x (1132.54 x - 20191.9) + 90001} + 300\right)^{-a}$
for $a>0$ but Wolfram Alpha doesn't give me a solution. It is however able to plot my equation (wolfram output). Am I doing something wrong and if not, is there another way to obtain a solution to this equation?
On
I tried your equation in Wolfram Mathematica and I got a solution but it's not a nice one (a whole screen full of numbers). However, if you just want to graph $x$ as a function of $a,$ I'd suggest you use some other program to make an image which you can use however you like. Here are a couple of examples from Wolfram Mathematica and GeoGebra. The latter is free.
That equation does not have a closed form expression (formula) for $a$ in terns of $x$ or $x$ in terms of $a$. If you know one of them you can use numerical methods to find the other. That's what Wolfram alpha is doing.