sqrt 3-x*2-x=x

To solve this equation, we can use algebraic manipulation:

1. Start by isolating the square root term on one side of the equation:

sqrt(3-x) = x + sqrt(2-x)

2. Square both sides of the equation to eliminate the square root:

3 - x = x^2 + 2 - x + 2x*sqrt(2-x)

3. Simplify the equation by combining like terms and isolating the radical term:

2x*sqrt(2-x) = x^2 + 1

4. Square both sides of the equation again to eliminate the radical:

4x^2 * (2-x) = (x^2 + 1)^2

5. Expand and simplify the equation:

-8x^3 + 4x^2 + 8x - 3 = 0

6. Factor the equation using synthetic division or trial and error:

(x-1)(-8x^2 + 12x + 3) = 0

7. Solve for x using the zero product property:

x = 1 or x = (3 + sqrt(33))/4 or x = (3 - sqrt(33))/4

Therefore, the solutions to the equation are x = 1, x = (3 + sqrt(33))/4, and x = (3 - sqrt(33))/4.