What is the general solution for 2sech^2(x)+tanh(x)=0 ?

The general solution for 2sech^2(x)+tanh(x)=0 is x= 1/2 ln(-4+sqrt(17))

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2sech^2(x)+tanh(x)=0

2 sech^{2} (x) + tanh (x) = 0

x = \frac{1}{2} ln (- 4 + 17)

Solution steps

2 sech^{2} (x) + tanh (x) = 0

Rewrite using trig identities

2 (\frac{2}{e ^{x} + e ^{- x}})^{2} + \frac{e ^{x} - e ^{- x}}{e ^{x} + e ^{- x}} = 0

2 (\frac{2}{e ^{x} + e ^{- x}})^{2} + \frac{e ^{x} - e ^{- x}}{e ^{x} + e ^{- x}} = 0 : x = \frac{1}{2} ln (- 4 + 17)

x = \frac{1}{2} ln (- 4 + 17)

8 cos (2 θ) = - 24 cos (θ) - 16

16 cos^{2} (θ) - 9 = 0

sin (a) + cos (a) = 1

2 sin^{2} (x) + 9 sin (x) - 5 = 0

10 cos (2 x) = 0

What is the general solution for 2sech^2(x)+tanh(x)=0 ?
The general solution for 2sech^2(x)+tanh(x)=0 is x= 1/2 ln(-4+sqrt(17))