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

What are the points of intersection of the line 2x plus 5y equals 4 with the curve y squared equals x plus 4?
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If: 2x +5y = 4 then 25y^2 = 4x^2 -16x +16If: y^2 = x +4 then 25y^2 = 25x +100So: 4x^2 -16x +16 = 25x +100Transposing terms: 4x^2 -41x -84 = 0Factorizing the above: (4x+7)(x-12) = 0 meaning x = -7/4 or x =12By substitution into original equation points of intersection:(-7/4, 3/2) and (12, -4)
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