For the following equation, state the value of the discriminant and then the nature of the soluation:

-3x^2-8x-11=0

Is there one real solution, two imaginary solutions or two real solutions?

d = b^2 - 4ac = 64 - 4(-3)(-11) = 64-132 = -68

since d < 0, there are two complex solutions

To find the value of the discriminant and determine the nature of the solutions, we need to use the quadratic formula. The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, the values are:
a = -3
b = -8
c = -11

To find the discriminant, which is the expression under the square root in the quadratic formula, we use the formula:

Discriminant (D) = b^2 - 4ac

Substituting the given values, we have:

D = (-8)^2 - 4(-3)(-11)

D = 64 - 132

D = -68

Therefore, the discriminant is -68.

Now, let's determine the nature of the solutions based on the value of the discriminant:

- If the discriminant (D) is greater than 0, then there are two real solutions.
- If the discriminant (D) is equal to 0, then there is one real solution.
- If the discriminant (D) is less than 0, then there are two imaginary solutions.

In this case, the discriminant is -68, which is less than 0. Therefore, the equation -3x^2 - 8x - 11 = 0 has two imaginary solutions.