x= 3 + sqrt(3x-5)

To solve the given equation, x = 3 + sqrt(3x - 5), we need to isolate the variable x on one side of the equation. Here's how you can do it step-by-step:

Step 1: Start by subtracting 3 from both sides of the equation:
x - 3 = sqrt(3x - 5)

Step 2: We want to eliminate the square root on the right-hand side of the equation. To do this, we need to square both sides of the equation:
(x - 3)^2 = (sqrt(3x - 5))^2

Simplifying the left-hand side:
(x - 3)(x - 3) = (3x - 5)

Expanding the left-hand side:
x^2 - 6x + 9 = 3x - 5

Step 3: Move all the terms involving x to one side of the equation by subtracting 3x from both sides:
x^2 - 6x + 9 - 3x = - 5

Simplifying:
x^2 - 9x + 9 = - 5

Step 4: Move the constant term (-5) to the other side of the equation by adding 5 to both sides:
x^2 - 9x + 9 + 5 = 0

Simplifying:
x^2 - 9x + 14 = 0

Step 5: Now, we need to factorize the quadratic equation:
(x - 2)(x - 7) = 0

Step 6: Use the zero product property to set each factor equal to zero:
x - 2 = 0 or x - 7 = 0

Step 7: Solve for x in each equation:
For x - 2 = 0:
x = 2

For x - 7 = 0:
x = 7

So, the solutions to the equation x = 3 + sqrt(3x - 5) are x = 2 and x = 7.