How to do it
In the Calculator app, type solve(, then the equation, then a comma, then the variable you're solving for, and close the bracket. Press enter and the TI-Nspire CX II CAS works it out.
You'll find the same command in the menu under menu → 3: Algebra → 1: Solve. The calculator then puts solve() in the entry line and you fill it in.
It's important that the equation really is an equation. solve(x^2-4,x) doesn't work, because there's no equals sign. It has to be solve(x^2-4=0,x). This is the most common mistake, and the calculator answers it with an argument error.
Why the variable has to go after the comma
The calculator doesn't know what you want to solve for, and it won't guess.
Take a*x+b=0. Write solve(a*x+b=0,x) and you get x in terms of a and b. Write solve(a*x+b=0,a) instead and you get a in terms of x and b. Same equation, two completely different answers, and the only difference is the letter after the comma.
With an equation that has only one letter, the variable looks unnecessary, and that's exactly why people forget it. Once there are parameters, it becomes clear what it's for.
What else the calculator shows you
It separates several solutions with “or”, for example x=-2 or x=2. That's an answer, not an error message.
If you get false, the equation has no solution. That's a result too. An equation like x^2=-1 simply has no solution in the real numbers, and the calculator tells you so.
Sometimes letters show up in the result that you never typed, often with a number after them. That happens with equations that have infinitely many solutions, typically with sine and cosine. The calculator then introduces its own helper variable that stands for any whole number.
Results come out exact, with fractions and roots. If you need a decimal, press ctrl and enter instead of enter. Same result, just rounded.