What is the general solution for 2cosh^2(x)-5sinh(x)=5 ?

The general solution for 2cosh^2(x)-5sinh(x)=5 is x=ln(0.61803…),x=ln(6.16227…)

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2cosh^2(x)-5sinh(x)=5

2 cosh^{2} (x) - 5 sinh (x) = 5

x = ln (0.61803 \dots), x = ln (6.16227 \dots)

Solution steps

2 cosh^{2} (x) - 5 sinh (x) = 5

Rewrite using trig identities

2 (\frac{e ^{x} + e ^{- x}}{2})^{2} - 5 \cdot \frac{e ^{x} - e ^{- x}}{2} = 5

2 (\frac{e ^{x} + e ^{- x}}{2})^{2} - 5 \cdot \frac{e ^{x} - e ^{- x}}{2} = 5 : x = ln (0.61803 \dots), x = ln (6.16227 \dots)

x = ln (0.61803 \dots), x = ln (6.16227 \dots)

10 + 5 cos (2 x) = 15 cos (x)

y, x = cos (2 y)

tan (x) = \frac{a}{b}

- 1 = cot (θ)

6 sin^{2} (A) - 5 sin (A) + 1 = 0

What is the general solution for 2cosh^2(x)-5sinh(x)=5 ?
The general solution for 2cosh^2(x)-5sinh(x)=5 is x=ln(0.61803…),x=ln(6.16227…)