What are the points of intersection of the line 2x plus 5y equals 4 with the curve y squared equals x plus 4?

If: 2x +5y = 4 then 25y^2 = 4x^2 -16x +16

If: y^2 = x +4 then 25y^2 = 25x +100

So: 4x^2 -16x +16 = 25x +100

Transposing terms: 4x^2 -41x -84 = 0

Factorizing the above: (4x+7)(x-12) = 0 meaning x = -7/4 or x = 12

By substitution into original equation points of intersection: (-7/4, 3/2) and (12, -4)