Solve the quadratic equation. \[ 3 x^{2}+9 x-1=0 \] Write one exact solution in each box. You can add or remove boxes. If there are no real solutions, remove all boxes.

To solve the quadratic equation \( 3x^{2} + 9x - 1 = 0 \), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Here, \( a = 3 \), \( b = 9 \), and \( c = -1 \). First, let's calculate the discriminant: \[ b^2 - 4ac = 9^2 - 4 \cdot 3 \cdot (-1) = 81 + 12 = 93 \] Since the discriminant is positive, there are two distinct real solutions. Now, we can plug the values into the quadratic formula: \[ x = \frac{-9 \pm \sqrt{93}}{2 \cdot 3} = \frac{-9 \pm \sqrt{93}}{6} \] The two solutions are: \[ x_1 = \frac{-9 + \sqrt{93}}{6} \] \[ x_2 = \frac{-9 - \sqrt{93}}{6} \] So, the exact solutions are: First Box: \( \frac{-9 + \sqrt{93}}{6} \) Second Box: \( \frac{-9 - \sqrt{93}}{6} \)