What is the answer to (x/(10))-20.89*e^{(-x)/((2478.82))}=0 ?

The answer to (x/(10))-20.89*e^{(-x)/((2478.82))}=0 is x=2478.82\W_{0}((208.9)/(2478.82))

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(x/(10))-20.89*e^{(-x)/((2478.82))}=0

(\frac{x}{10}) - 20.89 \cdot e^{\frac{- x}{( 2478.82 )}} = 0

x = 2478.82 W_{0} (\frac{208.9}{2478.82})

Decimal Notation

x = 193.23395 \dots

Solution steps

(\frac{x}{10}) - 20.89 e^{\frac{- x}{( 2478.82 )}} = 0

Prepare

(\frac{x}{10}) - 20.89 \cdot e^{\frac{- x}{( 2478.82 )}} = 0

for Lambert form:

- 208.9 = - e^{\frac{x}{2478.82}} x

Rewrite the equation with

\frac{x}{2478.82} = u

and

x = 2478.82 u

- 208.9 = - e^{u} \cdot 2478.82 u

Rewrite

- 208.9 = - e^{u} 2478.82 u

in Lambert form:

e^{u} u = \frac{208.9}{2478.82}

Solve

e^{u} u = \frac{208.9}{2478.82} : u = W_{0} (\frac{208.9}{2478.82})

u = W_{0} (\frac{208.9}{2478.82})

Substitute back

u = \frac{x}{2478.82},

solve for

x

Solve

\frac{x}{2478.82} = W_{0} (\frac{208.9}{2478.82}) : x = 2478.82 W_{0} (\frac{208.9}{2478.82})

x = 2478.82 W_{0} (\frac{208.9}{2478.82})

x, p^{2} - p (e^{x} + e^{- x}) + 1 = 0

2^{n - 1} = 16

14 e^{6 - x} + e^{12 x - 7} = 0

4 = x \cdot e^{x}

e^{l n (x) \cdot 10} = a

What is the answer to (x/(10))-20.89*e^{(-x)/((2478.82))}=0 ?
The answer to (x/(10))-20.89*e^{(-x)/((2478.82))}=0 is x=2478.82\W_{0}((208.9)/(2478.82))