Solve for x if 3cosh2x = 3+sinh x

Question

In 3cosh2x = 3+sinh x, what is the value of x?

Answer 1

3cosh2x = 3 + sinhx

3cosh2x -3 = sinhx

3(cosh2x-1) = sinhx

3sinh^2x = sinhx

3sinhx = 1

sinhx = 1/3

=>x = arcsinhx(1/3) = ln((1/3) + sqrt(x^2 +1))

or x = 0.327

Comments

Line but the last should be x = arcsinhx(1/3) = ln((1/3) + sqrt((1/3)^2 +1))