Solve equation by using the quadratic formula. List the solutions, separated by commas. Enter exact solutions. \( 3 x^{2}-x-1=0 \) \( x=\square \)

To solve the equation \( 3x^2 - x - 1 = 0 \) using the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), we identify the coefficients: \( a = 3 \), \( b = -1 \), and \( c = -1 \). Calculating the discriminant: \[ b^2 - 4ac = (-1)^2 - 4(3)(-1) = 1 + 12 = 13 \] Now, applying the quadratic formula: \[ x = \frac{-(-1) \pm \sqrt{13}}{2(3)} = \frac{1 \pm \sqrt{13}}{6} \] Thus, the solutions are: \[ x = \frac{1 + \sqrt{13}}{6}, \frac{1 - \sqrt{13}}{6} \]