Yes, but not in rational terms.
The factorisation is:
{x - [3-sqrt(57)]/6} * {x - [3+sqrt(57)]/6}
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The factors are -1(2x + 1)(3x + 4)
(x - 8)(3x + 4)
If the question could more exactly be phrased as, "What is the value of x when 9x2 - 16 = 0", the answer is, x = 4 or -4. This answer can be found by factoring 9x2 - 16 into (3x + 4)(3x - 4) and setting each factor equal to zero.
The sum of the coefficients is 3 - 7 + 4 = 0 so (x - 1) is a factor. Thus, 3x2 - 7x + 4 = 3x2 - 3x - 4x + 4 = 3x(x - 1) - 4(x - 1) = (3x - 4)(x - 1)
(x2 + 3x + 5)(x2 - 3x + 4)