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

The answer to 10x-20.89*e^{(-x)/((2478.82))}=0 is x=2478.82\W_{0}((20.89)/(24788.2))

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

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

x = 2478.82 W_{0} (\frac{20.89}{24788.2})

Decimal Notation

x = 2.08724 \dots

Solution steps

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

Prepare

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

for Lambert form:

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

Rewrite the equation with

\frac{x}{2478.82} = u

and

x = 2478.82 u

- 20.89 = - 10 e^{u} \cdot 2478.82 u

Rewrite

- 20.89 = - 10 e^{u} 2478.82 u

in Lambert form:

e^{u} u = \frac{20.89}{24788.2}

Solve

e^{u} u = \frac{20.89}{24788.2} : u = W_{0} (\frac{20.89}{24788.2})

u = W_{0} (\frac{20.89}{24788.2})

Substitute back

u = \frac{x}{2478.82},

solve for

x

Solve

\frac{x}{2478.82} = W_{0} (\frac{20.89}{24788.2}) : x = 2478.82 W_{0} (\frac{20.89}{24788.2})

x = 2478.82 W_{0} (\frac{20.89}{24788.2})

4^{x} = 5^{x + 1}

3^{x^{2} - 1} = 134

x^{x} = 100

y, e^{3 x} + x^{2} \cdot y + e^{y} = 0

7^{x} + 7^{x + 1} - 7^{x + 2} + 7^{x - 1} = - 286

What is the answer to 10x-20.89*e^{(-x)/((2478.82))}=0 ?
The answer to 10x-20.89*e^{(-x)/((2478.82))}=0 is x=2478.82\W_{0}((20.89)/(24788.2))