solve \( 5 k^{2}-22 k-15=0 \)

To solve the quadratic equation \( 5k^2 - 22k - 15 = 0 \), we can use the quadratic formula: \[ k = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Here, \( a = 5 \), \( b = -22 \), and \( c = -15 \). First, we calculate the discriminant: \[ b^2 - 4ac = (-22)^2 - 4(5)(-15) = 484 + 300 = 784 \] Now, plug in the values into the quadratic formula: \[ k = \frac{-(-22) \pm \sqrt{784}}{2(5)} = \frac{22 \pm 28}{10} \] This gives us two potential solutions: 1. \( k = \frac{22 + 28}{10} = \frac{50}{10} = 5 \) 2. \( k = \frac{22 - 28}{10} = \frac{-6}{10} = -0.6 \) Therefore, the solutions are: \[ k = 5 \quad \text{and} \quad k = -0.6 \]