To solve the quadratic equation \( x^2 + 9x - 15 = 0 \), we can use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Here, \( a = 1 \), \( b = 9 \), and \( c = -15 \).
- Calculate the discriminant \( b^2 - 4ac \):
\[ b^2 = 9^2 = 81 \] \[ 4ac = 4 \cdot 1 \cdot (-15) = -60 \] \[ b^2 - 4ac = 81 - (-60) = 81 + 60 = 141 \]
- Now, substitute \( a \), \( b \), and the discriminant into the quadratic formula:
\[ x = \frac{-9 \pm \sqrt{141}}{2 \cdot 1} = \frac{-9 \pm \sqrt{141}}{2} \]
Thus, the solutions to the quadratic equation are:
\[ x = \frac{-9 + \sqrt{141}}{2}, \quad x = \frac{-9 - \sqrt{141}}{2} \]
The correct option in your provided choices corresponds to:
\( x = \frac{-9 \pm \sqrt{141}}{2} \).