Find the domain of the function. \( f(x)=\frac{20}{x^{2}+5 x-150} \) What is the domain of \( f \) ? \( \square \) (Type your answer in interval notation.)

To find the domain of the function \( f(x)=\frac{20}{x^{2}+5x-150} \), we need to determine where the denominator is not equal to zero. So, we'll solve the equation \( x^{2}+5x-150=0 \) using the quadratic formula: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1, b = 5, c = -150 \). Calculating the discriminant: \( b^2 - 4ac = 5^2 - 4(1)(-150) = 25 + 600 = 625 \). Now, applying the quadratic formula yields \( x = \frac{-5 \pm 25}{2} \), giving us the roots \( x = 10 \) and \( x = -15 \). Thus, the function is undefined at these two points, so the domain of \( f \) excludes \( -15 \) and \( 10 \). Therefore, in interval notation, the domain of \( f \) is \( (-\infty, -15) \cup (-15, 10) \cup (10, \infty) \).