To solve this equation, we can start by simplifying the left side:

√(x-2) * √(4-x) = x^2 - 6x + 10

Since the square root of a product is equal to the product of the square roots, we can rewrite the left side as:

√[(x-2) * (4-x)] = x^2 - 6x + 10

Next, we can multiply out the expression inside the square root:

√[4x - x^2 - 8 + 2x] = x^2 - 6x + 10

Simplifying further:

√[-x^2 + 6x - 8] = x^2 - 6x + 10

Now, let's square both sides of the equation to eliminate the square root:

[-x^2 + 6x - 8] = (x^2 - 6x + 10)^2

Expanding the right side:

[-x^2 + 6x - 8] = x^4 - 12x^3 + 46x^2 - 120x + 100

Rearranging the terms:

x^4 - 12x^3 + 46x^2 - 120x + 100 + x^2 - 6x + 8 = 0

Combining like terms:

x^4 - 12x^3 + 47x^2 - 126x + 108 = 0

Unfortunately, this equation does not have a simple solution. It is a quartic equation, which means it has a degree of 4 and can be difficult to solve algebraically. You may need to use numerical methods or a graphing calculator to find the approximate solutions.