Solve the Quadratic Equation: -6x² + 12x - 14 = 0

To solve the quadratic equation $-6x^2 + 12x - 14 = 0$, we'll use the quadratic formula:

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Let's calculate step by step:

• Identify the coefficients: Here, $a = -6$, $b = 12$, and $c = -14$.
• Compute the discriminant: $b^2 - 4ac = 12^2 - 4(-6)(-14) = 144 - 336 = -192$.
• Assess the discriminant: The discriminant is $-192$, which is less than zero.
• Since the discriminant is negative, there are no real solutions to the equation.

Therefore, the correct answer to the problem is "No solution."