Tìm x:

To solve the equation 2x^2 - 5x - 4 + 3√(2x - 1) = 0, we can follow these steps:

1. Move the constant term to the right side of the equation:
2x^2 - 5x + 3√(2x - 1) = 4

2. Isolate the radical term by subtracting 4 from both sides:
2x^2 - 5x + 3√(2x - 1) - 4 = 0

3. Square both sides of the equation to eliminate the radical:
(2x^2 - 5x + 3√(2x - 1) - 4)^2 = 0

4. Expand the squared term:
4x^4 - 20x^3 + 36x^2 - 16x + 24√(2x - 1) - 30x√(2x - 1) + 9(2x - 1) - 8√(2x - 1) + 16 = 0

5. Combine like terms:
4x^4 - 20x^3 + 36x^2 - 46x + 9(2x - 1) + 16 + 16√(2x - 1) = 0

6. Simplify:
4x^4 - 20x^3 + 36x^2 - 46x + 18x - 9 + 16 + 16√(2x - 1) = 0

7. Combine like terms:
4x^4 - 20x^3 + 36x^2 - 28x + 25 + 16√(2x - 1) = 0

At this point, the equation becomes a quartic equation, which can be difficult to solve algebraically. You may need to use numerical methods or a graphing calculator to find the approximate solutions.