x*(2.71828^x)=0.002

Solution for x*(2.71828^x)=0.002 equation:

x(2.71828^x)=0.002

We move all terms to the left:

x(2.71828^x)-(0.002)=0

We add all the numbers together, and all the variables

x(2.71828^x)-0.002=0

We multiply parentheses

2x^2-0.002=0

a = 2; b = 0; c = -0.002;
Δ = b2-4ac
Δ = 02-4·2·(-0.002)
Δ = 0.016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-\sqrt{0.016}}{2*2}=\frac{0-\sqrt{0.016}}{4}
=-\frac{\sqrt{}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{0.016}}{2*2}=\frac{0+\sqrt{0.016}}{4}
=\frac{\sqrt{}}{4}
$