Find the $x$-locations of intersection for $y=x^{2}-3 x-7$ and $y=2 x^{2}+8 x+3$

Step 1 ：Set the two functions equal to each other: \(x^{2} - 3x - 7 = 2x^{2} + 8x + 3\)

Step 2 ：Solve the resulting quadratic equation for x using the quadratic formula.

Step 3 ：The solutions to the equation are x = -10 and x = -1.

Step 4 ：These are the x-locations of the intersection points of the two functions.

Step 5 ：Final Answer: The x-locations of the intersection points are \(\boxed{-10}\) and \(\boxed{-1}\).