Evaluate the discriminant for the equation. Determine the number of real solutions.
6x^2 + 5x + 6 = 0
The discriminant is given by the formula:
Δ = b^2 - 4ac
For the equation 6x^2 + 5x + 6 = 0, we have:
a = 6, b = 5, c = 6
Δ = (5)^2 - 4(6)(6)
= 25 - 144
= -119
Since the discriminant is negative (Δ < 0), there are no real solutions to the equation.