Solve the Quadratic Equation: 3x² - 9x + 12 = 0

Solve the equation

$3x^2-9x+12=0$

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

• Step 1: Identify the coefficients $a = 3$, $b = -9$, $c = 12$.
• Step 2: Compute the discriminant $\Delta = b^2 - 4ac$.
• Step 3: Determine if real solutions exist based on the discriminant.
• Step 4: Solve using the Quadratic Formula if applicable.

Now, let's work through each step:

Step 2: Calculate the discriminant:

$\Delta = (-9)^2 - 4 \times 3 \times 12$

$\Delta = 81 - 144 = -63$

Step 3: Since the discriminant $\Delta$ is negative ($-63$), this means there are no real solutions for the quadratic equation. A negative discriminant indicates that the solutions are complex (i.e., non-real), so the equation has no real solution.

Therefore, the solution to the problem is No solution.