The graphs of y= x^2 - 8x - 35 and

Question

y= -2(x^2) + 16x +3 intersect in two points. What is the sum of the x-coordinates of the two points of intersection?

Answer 1

Equate the two equation to get:
x^2 - 8x - 35=-2(x^2) + 16x +3
Arrange terms and solve the quadratic equation using the quadratic formula (or otherwise) to get:
x=(-sqrt(258)+12)/3 and
x=(sqrt(258)+12)/3

The sum of the two roots give
24/3 = 8