Solve equation by using the quadratic formula. List the solutions, separated by commas. Enter exact solutions. \( 4 p^{2}-p-1=0 \) \( p=\square \)

To solve the equation \( 4p^2 - p - 1 = 0 \) using the quadratic formula \( p = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), we first identify the coefficients: \( a = 4 \), \( b = -1 \), and \( c = -1 \). We calculate the discriminant: \( b^2 - 4ac = (-1)^2 - 4(4)(-1) = 1 + 16 = 17 \). Now, substituting the values into the quadratic formula gives: \( p = \frac{-(-1) \pm \sqrt{17}}{2 \cdot 4} \) \( p = \frac{1 \pm \sqrt{17}}{8} \). So, the solutions are: \( p = \frac{1 + \sqrt{17}}{8}, \frac{1 - \sqrt{17}}{8} \).