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coordinate geometry intersecting line and curves helpp core 1

Would anyone mind helping me with the method for solving this intersecting lines and curves question?
I missed all the intersection lessons and I'm so confused.

Find the x-coordinates of the points of intersection of the line y = 3x + 2
and the curve y=3x^2 - 7x + 1. Leave your answer in surd form.

I tried to make them = to eachother by saying 3x + 2 = 3x^2 - 7x + 1
then I formed a quadratic and got :
3x^2 - 10x - 1 = 0

because the question said to leave my answer in surd form, I tried to use the quadratic formula and ended up with 5 +- 2 (sqrt)/ 3
but I think this is all wrong...

please helpp
Original post by wednesday_adams
...


Your answer is incomplete but the correct solution is something of the form 5±2a3 \dfrac {5 \pm 2 \sqrt a}{3} where a is an integer.

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