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:

\[ y = 6 \quad \text{and} \quad y = -5 \]