Points: 0 of 2 Sav Solve the equation using the quadratic formula. $$ x^{2}+13 x+7=0 $$ The solution set is $$ \square $$ \}. (Simplify your answer. Type an exact answer, using radicals and $$ i $$ as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

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To solve the quadratic equation $$ x^{2} + 13x + 7 = 0 $$ using the quadratic formula, follow these steps:

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

Here, the coefficients are:
- $$ a = 1 $$
- $$ b = 13 $$
- $$ c = 7 $$

1. **Calculate the discriminant ($$ \Delta $$):**
$$
\Delta = b^{2} - 4ac = 13^{2} - 4(1)(7) = 169 - 28 = 141
$$

2. **Apply the quadratic formula:**
$$
x = \frac{-13 \pm \sqrt{141}}{2}
$$

So, the solution set is:
$$
\left\{ \frac{-13 + \sqrt{141}}{2}, \frac{-13 - \sqrt{141}}{2} \right\}
$$

In the required format, the solution set is:
$$
\frac{-13 + \sqrt{141}}{2}, \frac{-13 - \sqrt{141}}{2}
$$
The solutions are $$ \frac{-13 + \sqrt{141}}{2} $$ and $$ \frac{-13 - \sqrt{141}}{2} $$.

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