Solving the Equation x = 3x²: No Solutions

The equation 'x = 3x²' has no real solutions. Here's why:

1. Rearranging the equation: Subtract 'x' from both sides to get '0 = 3x² - x'.
2. Quadratic formula: This equation is in the standard quadratic form (ax² + bx + c = 0). We can use the quadratic formula to find the solutions: x = (-b ± √(b² - 4ac)) / 2a In this case, a = 3, b = -1, and c = 0.
3. Discriminant: The discriminant (b² - 4ac) tells us the nature of the solutions. If the discriminant is negative, there are no real solutions. In this case, the discriminant is (-1)² - 4 * 3 * 0 = 1. Since the discriminant is positive, there are real solutions. However, the solutions are complex numbers, not real numbers.

Therefore, the equation 'x = 3x²' has no real solutions.