Tìm x: - 3√(2 |2x + 1| - 5) + 6x + 3 = 0

To solve the equation, we need to isolate the variable x. Let's start by simplifying the equation:

-3√(2 |2x + 1| - 5) + 6x + 3 = 0

First, let's remove the square root by squaring both sides of the equation:

(-3√(2 |2x + 1| - 5))^2 = (6x + 3)^2

9(2 |2x + 1| - 5) = (6x + 3)^2

Now, let's simplify further:

18 |2x + 1| - 45 = 36x^2 + 36x + 9

18 |2x + 1| = 36x^2 + 36x + 54

Divide both sides by 18:

|2x + 1| = 2x^2 + 2x + 3

Now, we have two cases to consider:

Case 1: 2x + 1 ≥ 0

In this case, the absolute value can be removed:

2x + 1 = 2x^2 + 2x + 3

Rearrange the equation:

2x^2 + 2x + 3 - 2x - 1 = 0

2x^2 + 2 = 0

Divide both sides by 2:

x^2 + 1 = 0

This equation has no real solutions since x^2 + 1 is always positive.

Case 2: 2x + 1 < 0

In this case, the absolute value becomes negative:

-(2x + 1) = 2x^2 + 2x + 3

Distribute the negative sign:

-2x - 1 = 2x^2 + 2x + 3

Rearrange the equation:

2x^2 + 4x + 4 = 0

Divide both sides by 2:

x^2 + 2x + 2 = 0

This quadratic equation does not factor, so we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 2, and c = 2:

x = (-2 ± √(2^2 - 4(1)(2))) / (2(1))

x = (-2 ± √(4 - 8)) / 2

x = (-2 ± √(-4)) / 2

Since the square root of a negative number is not a real number, there are no real solutions in this case.

Therefore, the equation -3√(2 |2x + 1| - 5) + 6x + 3 = 0 has no real solutions.