Find the points where these conics intercept:

16x^2 - 5y^2 = 64
16x^2 + 25y^2 - 96x = 256

Multiply the first equation by 5 and add to the second

96x^2-96x=576
x^2 -x=6
x^2 - x -6=0
(x-3)(x+2)=0
x=3 or x = -2
points (3, 4), (3,-4) and (-2,0)