solve 3sinh^2(2x) + 11sinh(2x) = 4 for x, giving your answer(s) in terms of the natural log.

3sinh^2(2x) + 11sinh(2x) - 4 = 0 --> (3sinh(2x) - 1)(sinh(2x) + 4) = 0 --> sinh(2x) = 1/3, sinh(2x) = -4(e^(2x) - e^(-2x))/2 = 1/3 --> e^(4x) -(2/3)e^(2x) - 1 = 0 --> e^(2x) = 1/3 + 2sqrt(5)/3 the other solution is negative, e^2x > 0--> x = (1/2)ln(1/3 + 2sqrt(5)/3)(e^(2x) - e^(-2x))/2 = -4 --> e^(4x) - 8e^(2x) - 1 = 0 --> e^(2x) = 4 + sqrt(34) sqrt(34) > 4 so other solution is negative--> x = (1/2)ln(4 + sqrt(34))