Consider the quadratic equation. $$ -t^{2}-9 t-7=0 $$ State the values of $$ a, b, c $$, in the standard form of a quadratic equation. $$ a=\square $$ $$ b=\square $$ Determine the value of the discriminant, $$ D=\square $$ Since the discriminant is Select an answer $$ \vee $$, there will be Hint: Enter the number of real solutions.

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To analyze the quadratic equation $$ -t^{2}-9t-7=0 $$, we first need to express it in the standard form of a quadratic equation, which is given by:

$$
at^2 + bt + c = 0
$$

From the equation $$ -t^{2}-9t-7=0 $$, we can identify the coefficients:

1. $$ a = -1 $$
2. $$ b = -9 $$
3. $$ c = -7 $$

Now, we can summarize the values:

$$
a = -1
$$
$$
b = -9
$$
$$
c = -7
$$

Next, we will calculate the discriminant $$ D $$ using the formula:

$$
D = b^2 - 4ac
$$

Substituting the values of $$ a $$, $$ b $$, and $$ c $$:

$$
D = (-9)^2 - 4(-1)(-7)
$$

Now, let's calculate $$ D $$:

$$
D = 81 - 28
$$
$$
D = 53
$$

Now we have:

$$
D = 53
$$

Since the discriminant $$ D $$ is greater than zero ($$ D > 0 $$), this indicates that there will be two distinct real solutions.

To summarize:

- The values are:
  - $$ a = -1 $$
  - $$ b = -9 $$
  - $$ c = -7 $$
  
- The value of the discriminant is:
  - $$ D = 53 $$

- Since the discriminant is greater than zero, there will be **two distinct real solutions**.
$$ a = -1 $$, $$ b = -9 $$, $$ c = -7 $$, $$ D = 53 $$, and there are two distinct real solutions.

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