To solve the equation, we need to simplify both sides and then solve for x.

Starting with the left side of the equation:
(9-2x)^4

Using the exponent rule for a power of a binomial, we can expand this expression:
(9-2x)^4 = 9^4 - 4 * 9^3 * 2x + 6 * 9^2 * (2x)^2 - 4 * 9 * (2x)^3 + (2x)^4
= 6561 - 4 * 729 * 2x + 6 * 81 * 4x^2 - 4 * 9 * 8x^3 + 16x^4
= 6561 - 5832x + 1944x^2 - 288x^3 + 16x^4

Now let's simplify the right side of the equation:
626 - 1^2022 = 626 - 1 = 625

So the equation becomes:
6561 - 5832x + 1944x^2 - 288x^3 + 16x^4 = 625

Rearranging the equation to set it equal to zero:
16x^4 - 288x^3 + 1944x^2 - 5832x + 5936 = 0

Unfortunately, this equation cannot be easily factored or solved algebraically. It may require the use of numerical methods or a graphing calculator to find the approximate solutions.