Y^2-y-30=0

To solve the quadratic equation \( y^2 - y - 30 = 0 \), you can use the quadratic formula: \[ y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] In the equation \( y^2 - y - 30 = 0 \), the coefficients are: - \( a = 1 \) - \( b = -1 \) - \( c = -30 \) Now, plug these values into the formula: 1. Calculate the discriminant \( b^2 - 4ac \): \[ b^2 - 4ac = (-1)^2 - 4 \cdot 1 \cdot (-30) = 1 + 120 = 121 \] 2. Now compute \( y \): \[ y = \frac{-(-1) \pm \sqrt{121}}{2 \cdot 1} = \frac{1 \pm 11}{2} \] This gives us two solutions: \[ y = \frac{1 + 11}{2} = \frac{12}{2} = 6 \] \[ y = \frac{1 - 11}{2} = \frac{-10}{2} = -5 \] Thus, the solutions to the equation \( y^2 - y - 30 = 0 \) are: \[ y = 6 \quad \text{and} \quad y = -5 \]