Set the equations each to each other and solve for x f(x) = g(x) x^2 - 3x = 2x+14 x^2-3x-2x-14 = 0 x^2-5x-14 = 0 .... see note below (x-7)(x+2) = 0 x-7 = 0 or x+2 = 0 x = 7 or x = -2 The two solutions are x = 7 or x = -2
note: we technically could stop at this line and divert to another path. Instead of finding the actual solutions, we can use the discriminant formula d = b^2 - 4ac to find the value of d. It turns out that d = (-5)^2 - 4(1)(-14) d = 81 which is a positive number. So that shows we have two solutions.
