\( 1 \leftarrow \) Find the real solutions, if any, of the following equation. Use the quadratic formula. \( x^{2}-\sqrt{3} x-2=0 \) Select the correct choice below and, if necessary, fill in the answer box to complete your answer. A. Simplify your answer. Type an integer or decimal rounded to two decimal places as needed. Use a comma to separate answers as needed.) B. The solution is not a real number.

To solve the equation \( x^{2}-\sqrt{3} x-2=0 \) using the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), we identify \( a = 1 \), \( b = -\sqrt{3} \), and \( c = -2 \). Plugging in these values, we find: 1. The discriminant \( b^2 - 4ac = (\sqrt{3})^2 - 4(1)(-2) = 3 + 8 = 11 \). 2. Thus, \( x = \frac{\sqrt{3} \pm \sqrt{11}}{2} \). Calculating the two solutions, we get approximately \( x_1 \approx 2.33 \) and \( x_2 \approx -0.33 \). So, the simplified solution is \( \frac{\sqrt{3} + \sqrt{11}}{2}, \frac{\sqrt{3} - \sqrt{11}}{2} \). If you need the numerical values to two decimal places, the answers are \( 2.33, -0.33 \).