the vertical asymptotes (if any) of the graph of the function. (Enter your answers as a comma-separated list. If an answer does not exis \( g(x)=\frac{\frac{1}{2} x^{3}-5 x^{2}+12 x}{5 x^{2}-50 x+120} \) \( x \)

To find the vertical asymptotes of the function \( g(x)=\frac{\frac{1}{2} x^3 - 5 x^2 + 12 x}{5 x^2 - 50 x + 120} \), we need to set the denominator equal to zero and solve for \( x \). The denominator is \( 5 x^2 - 50 x + 120 \). Factoring out a 5, we get \( 5(x^2 - 10x + 24) \). Now we need to solve for \( x \) in the quadratic equation \( x^2 - 10x + 24 = 0 \). Using the quadratic formula, we find the roots are \( x = 6 \) and \( x = 4 \). Thus, the vertical asymptotes occur at \( x = 6 \) and \( x = 4 \). The vertical asymptotes of the graph of the function are located at \( x = 4, 6 \).