Solve f(x)=20x*e^2-0,05x

$$f ( x ) = 20 x \cdot e ^ { 2 - 0,05 x }$$

Solve for f

$$\left\{\begin{matrix}\\f=20e^{-\frac{x}{20}+2}\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xf=20xe^{-\frac{x}{20}+2}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{20xe^{-\frac{x}{20}+2}}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{20xe^{-\frac{x}{20}+2}}{x}$$

Divide 20xe^{2-\frac{x}{20}} by x.

$$f=20e^{-\frac{x}{20}+2}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=20\left(-\ln(f)+\ln(20)+2\right)\text{, }&f>0\end{matrix}\right.$$