So 0 = 3x² + 6x - 7

Like you said (or implied), it won't factorize so we should use the quadratic formula to solve it.

x = [-6 +/- sqrt(6² - 4(3 x -7))] / 2(3)

x = [-6 +/- sqrt(120)] / 6

x = [-6 +/- 2sqrt(30)] / 6

x = [-3 +/- sqrt(30)] / 3

x = -1 +/- sqrt(30)/3

So those are your two answers.

x = -1 + sqrt(30)/3 or
x = -1 - sqrt(30)/3

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