Use the quadratic formula to solve the equation. \( y^{2}-8 y=-11 \)

To solve the equation \( y^{2}-8y=-11 \), first move all terms to one side to set it to zero: \( y^{2}-8y + 11 = 0 \). Now, we can use the quadratic formula \( y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) where \( a = 1 \), \( b = -8 \), and \( c = 11 \). Calculating the discriminant: \( b^2 - 4ac = (-8)^2 - 4(1)(11) = 64 - 44 = 20 \). Now plug everything into the formula: \( y = \frac{-(-8) \pm \sqrt{20}}{2(1)} = \frac{8 \pm \sqrt{20}}{2} \). Since \( \sqrt{20} = 2\sqrt{5} \), we simplify: \( y = \frac{8 \pm 2\sqrt{5}}{2} = 4 \pm \sqrt{5} \). Thus, the solutions are: \( y = 4 + \sqrt{5} \) and \( y = 4 - \sqrt{5} \).