Use the Quadratic Formula to solve the equation. (Enter your answers as a comma-separated list.) \[ 25 h^{2}+80 h=-57 \] \( h=\square \)

To solve the equation \( 25h^2 + 80h + 57 = 0 \) using the quadratic formula \( h = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), you first identify \( a = 25 \), \( b = 80 \), and \( c = 57 \). Calculating the discriminant: \( b^2 - 4ac = 80^2 - 4 \times 25 \times 57 = 6400 - 5700 = 700 \). Now, plugging the values into the quadratic formula: \( h = \frac{-80 \pm \sqrt{700}}{2 \times 25} = \frac{-80 \pm 10\sqrt{7}}{50} \). Simplifying gives: \( h = \frac{-8 \pm \sqrt{7}}{5} \), resulting in two solutions: \( h = \frac{-8 + \sqrt{7}}{5}, \frac{-8 - \sqrt{7}}{5} \). So the solutions are: \( h = \frac{-8 + \sqrt{7}}{5}, \frac{-8 - \sqrt{7}}{5} \).