To solve this equation for x, we need to use inverse trigonometric functions. Specifically, we can use the inverse sine function (sin??).

First, we need to isolate the sin function by subtracting p/3 from both sides of the equation:

sin(x + p/3) - p/3 = sqrt(3)/2

Next, we can take the inverse sine of both sides:

sin??(sin(x + p/3) - p/3) = sin??(sqrt(3)/2)

Using the identity sin??(sin(a)) = a, we can simplify the left-hand side:

x + p/3 - p/3 = sin??(sqrt(3)/2)

Simplifying further:

x = sin??(sqrt(3)/2) - p/3

Using a calculator, we can evaluate the inverse sine of sqrt(3)/2 to get:

x = pi/3 - p/3

So the solution for x is:

x = (pi - p) / 3

Note that there are an infinite number of solutions for x, because the sine function has a period of 2pi. So any value of x that satisfies the equation:

x + p/3 = n*2pi + pi/3, where n is an integer,

will also be a solution.