How do I find the intersection between $f(x) = 3(x-2)^2$ and $g(x) = 3\sin(x-4)$? It's a sinusodial function so it I couldn't solve it like a normal intersection.
This leads to a transcendental equation. Typically, you can find approximate solutions for these using numerical root-finding algorithms, like Newton's method or Bisection method.
Typically, an anlytical solution to these could be expressed using special functions, but they don't have nice closed form.
However, in your case, it is easy to prove that, in fact, no solutions exists at all in the real numbers (there are complex ones, though) -- since f(x) is always above g(x).