Find all x-intercepts of the following function. Write your answer or answers as coordinate points. Be sure to select the appropriate number of \( x \)-intercepls. \[ f(x)=\frac{3 x^{2}+5 x-28}{2 x^{2}+18 x-20} \]

To find the \( x \)-intercepts of the function \( f(x) = \frac{3x^2 + 5x - 28}{2x^2 + 18x - 20} \), we need to set the numerator of the function equal to zero and solve for \( x \). The numerator of the function is \( 3x^2 + 5x - 28 \). To find the \( x \)-intercepts, we set this expression equal to zero and solve for \( x \): \[ 3x^2 + 5x - 28 = 0 \] Now, we can solve this quadratic equation to find the \( x \)-intercepts. Solve the quadratic equation by following steps: - step0: Solve by factoring: \(3x^{2}+5x-28=0\) - step1: Factor the expression: \(\left(x+4\right)\left(3x-7\right)=0\) - step2: Separate into possible cases: \(\begin{align}&3x-7=0\\&x+4=0\end{align}\) - step3: Solve the equation: \(\begin{align}&x=\frac{7}{3}\\&x=-4\end{align}\) - step4: Rewrite: \(x_{1}=-4,x_{2}=\frac{7}{3}\) The \( x \)-intercepts of the function \( f(x) = \frac{3x^2 + 5x - 28}{2x^2 + 18x - 20} \) are \( (-4, 0) \) and \( \left(\frac{7}{3}, 0\right) \).