To solve this equation, we first need to find the sum of the geometric series on the left side of the equation.

The sum of a geometric series with first term a, common ratio r, and n terms is given by the formula:

S = a(1 - r^n) / (1 - r)

In this case, a = 4, r = 2, and n = 20. Plugging these values into the formula, we get:

S = 4(1 - 2^20) / (1 - 2)
S = 4(1 - 1048576) / -1
S = 4(-1048575) / -1
S = -4194300

Now we can substitute this sum back into the original equation:

-4194300x = 2^22 - 2^21

Now we can simplify the right side of the equation:

2^22 - 2^21 = 2^21(2 - 1) = 2^21

Substitute this back into the equation:

-4194300x = 2^21

Now we can solve for x:

x = 2^21 / -4194300
x = 2097152 / -4194300
x = -0.5

Therefore, the solution to the equation is x = -0.5.