Solving the Quadratic Equation: x = 3x^2 + 2

To solve the equation x = 3x^2 + 2, follow these steps:

1. Rearrange the equation: Subtract x from both sides to get a standard quadratic equation: 0 = 3x^2 - x + 2

2. Solve for x using the quadratic formula: The quadratic formula is used to find the solutions (roots) of a quadratic equation in the form ax^2 + bx + c = 0: x = (-b ± √(b^2 - 4ac)) / 2a

   In this case, a = 3, b = -1, and c = 2. Substitute these values into the quadratic formula: x = (1 ± √((-1)^2 - 4 * 3 * 2)) / (2 * 3) x = (1 ± √(-23)) / 6

3. Simplify the solution: The square root of -23 is an imaginary number. Therefore, the solutions for x are complex numbers: x = (1 ± i√23) / 6

   Where 'i' represents the imaginary unit (√-1).

Therefore, the solutions to the equation x = 3x^2 + 2 are x = (1 + i√23) / 6 and x = (1 - i√23) / 6.