solve. If the equation has no real solutions, say so.

Square root of 3x+4= x

To solve the equation √(3x+4) = x, we'll need to isolate the variable x on one side of the equation. Let's break down the steps:

1. Square both sides of the equation to eliminate the square root: (√(3x+4))^2 = x^2
Simplifying, we have 3x + 4 = x^2

2. Rearrange the equation to bring all terms to one side:
x^2 - 3x - 4 = 0

3. Now, we have a quadratic equation. To solve it, we can either factor it or use the quadratic formula. Let's factor it:

(x - 4)(x + 1) = 0

Setting each factor equal to zero:
x - 4 = 0 or x + 1 = 0

Solving for x in each case:
x = 4 or x = -1

Thus, we have two possible solutions: x = 4 and x = -1.

To verify if these solutions are valid, we substitute them back into the original equation:

For x = 4: Square root of (3(4) + 4) = 4
√(12 + 4) = 4
√16 = 4
4 = 4

For x = -1: Square root of (3(-1) + 4) = -1
√(-3 + 4) = -1
√1 = -1
1 = -1

From the verification, we can see that neither x = 4 nor x = -1 is a valid solution. Therefore, the equation has no real solutions.