2√x-x^2 =3(√x +√1-x -1 )

To solve this equation, we can first simplify both sides:

2√x - x^2 = 3(√x + √(1-x) - 1)

Expand the right side:

2√x - x^2 = 3√x + 3√(1-x) - 3

Now, let's isolate the square root terms on one side of the equation:

2√x - 3√x = x^2 + 3√(1-x) - 3

Simplify the square root terms:

-√x = x^2 + 3√(1-x) - 3

Now, square both sides to eliminate the square root:

(-√x)^2 = (x^2 + 3√(1-x) - 3)^2

x = x^4 + 9(1-x) + 9 - 6x^2√(1-x)

Now, we have a quartic equation in terms of x. We can simplify this further by expanding and rearranging the terms:

x = x^4 + 9 - 9x + 9 - 6x^2√(1-x)

x = x^4 - 6x^2√(1-x) - 9x + 18

This equation does not have a simple solution and may require numerical methods to find the value of x that satisfies the equation.