To solve this equation, we need to first simplify the left side of the equation:

cos(4x - 10) / 4 = √2 / 2

Dividing both sides by 1/4 (or multiplying both sides by 4), we get:

cos(4x - 10) = 2√2

To find the value of x, we need to take the inverse cosine of both sides:

4x - 10 = arccos(2√2)

Now, isolate x by solving for x:

4x = 10 + arccos(2√2)

x = (10 + arccos(2√2)) / 4

This is the solution for x in the given equation.