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**mark** prove that the line with the equation $\displaystyle x + 2y = 2$ and the curve with equation $\displaystyle y = 3x^2 - 2x + 2$ have no points of intersection

i started by putting the first equation into the second after making the first equation $\displaystyle x = 2 - 2y$. so it became $\displaystyle 3(2 - 2y)^2 - 2(2 - 2y) + 2$ then expanded the brackets. so first i squared the first bracketed term and made it $\displaystyle 3(4 - 8y + 4y^2)$ then expanded the second and made it $\displaystyle (4 - 4y)$ so i was left with $\displaystyle (12 - 24y + 12y^2) - (4 - 4y) + 2$ which then came to $\displaystyle 12y^2 - 20y + 10$ and used the discriminant theory to make sure it came to less than 0. i came up with $\displaystyle 400 - 480$ for the discriminant. so -80 was the discriminant. but my book says its -39. can someone explain where i went wrong with this? thanks