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exp(x/2)-(2/(5*x))=0 equation

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Numerical solution:

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The solution

You have entered [src]
 x          
 -          
 2    2     
e  - --- = 0
     5*x    
$$e^{\frac{x}{2}} - \frac{2}{5 x} = 0$$
The graph
Rapid solution [src]
x1 = 2*W(1/5)
$$x_{1} = 2 W\left(\frac{1}{5}\right)$$
x1 = 2*LambertW(1/5)
Sum and product of roots [src]
sum
2*W(1/5)
$$2 W\left(\frac{1}{5}\right)$$
=
2*W(1/5)
$$2 W\left(\frac{1}{5}\right)$$
product
2*W(1/5)
$$2 W\left(\frac{1}{5}\right)$$
=
2*W(1/5)
$$2 W\left(\frac{1}{5}\right)$$
2*LambertW(1/5)
Numerical answer [src]
x1 = 0.337831946998219
x1 = 0.337831946998219