If you mean 3x - 11 = 1 / (3x - 8), we have:
3x - 11 = 1 / (3x - 8), x =/= 8/3
(3x - 11)(3x - 8) = 1
9x^2 - 33x - 24x + 88 = 1
9x^2 - 57x + 87 = 0
Using the quadratic formula, we have:
x = [57 +/- sqrt((-57)^2 - 4(9)(87))] / [2(9)]
x = [57 +/- sqrt(117)] / [18]
x = 3[19 +/- sqrt(13)] / [3 * 6]
x = [19 +/- sqrt(113)] / 6
Suppose you meant 3x - 11 = (1 / 3x) - 8 instead. We will have:
3x - 11 = (1 / 3x) - 8, x =/= 0
[(3x - 11)(3x)] / (3x) = (1 / 3x) - ([(8)(3x)] / (3x))
(3x - 11)(3x) = 1 - (8)(3x)
9x^2 - 33x = 1 - 24x
9x^2 - 9x - 1 = 0
Using the quadratic formula, we have:
x = [9 +/- sqrt((-9)^2 - 4(9)(-1))] / [2(9)]
x = [9 +/- sqrt(117)] / [18]
x = 3[3 +/- sqrt(13)] / [(3)(6)]
x = [3 +/- sqrt(13)] / 6