Solve the quadratic equation. \[ 3 x^{2}+8 x-13=0 \] Write one exact solution in each box. You can add or remove boxes. If there are solutions, remove all boxes.

To solve the quadratic equation \(3x^{2}+8x-13=0\), we can apply the quadratic formula, which is given by \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Here, \(a = 3\), \(b = 8\), and \(c = -13\). Plugging these values into the formula: 1. Calculate the discriminant: \[ b^2 - 4ac = 8^2 - 4 \cdot 3 \cdot (-13) = 64 + 156 = 220 \] 2. Now substitute back into the quadratic formula: \[ x = \frac{-8 \pm \sqrt{220}}{2 \cdot 3} = \frac{-8 \pm \sqrt{4 \cdot 55}}{6} = \frac{-8 \pm 2\sqrt{55}}{6} = \frac{-4 \pm \sqrt{55}}{3} \] Thus, the exact solutions are: \[ x = \frac{-4 + \sqrt{55}}{3} \] and \[ x = \frac{-4 - \sqrt{55}}{3} \]