Solve the Quadratic Equation: 3x² + 7 = 2x² + 9

To solve this problem, we'll follow these steps:

• Simplify the given expression.
• Rearrange into standard quadratic form.
• Solve using applicable method.

Let's begin the process:
1. Simplify the left-hand side: $x \cdot 3 \cdot x + 7 = 3x^2 + 7$.

2. Set up the equation by balancing: $3x^2 + 7 = 2x^2 + 9$.

3. Rearrange the terms to form a quadratic equation: $3x^2 - 2x^2 + 7 - 9 = 0$.

This simplifies to: $x^2 - 2 = 0$.

4. Solve for $x$:
By adding 2 to both sides, we have: $x^2 = 2$.
Take the square root of both sides: $x = \pm\sqrt{2}$.

Therefore, the solution to the problem is $\pm\sqrt{2}$.