Solve (1+0.4/sqrt{3})x=5000

$$( 1 + \frac { 0.4 } { \sqrt { 3 } } ) x = 5000$$

Solve for x

$$x = \frac{375000 - 50000 \sqrt{3}}{71} \approx 4061.936051008$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{0.4}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\left(1+\frac{0.4\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)x=5000$$

The square of \sqrt{3} is 3.

$$\left(1+\frac{0.4\sqrt{3}}{3}\right)x=5000$$

Divide 0.4\sqrt{3} by 3 to get \frac{2}{15}\sqrt{3}.

$$\left(1+\frac{2}{15}\sqrt{3}\right)x=5000$$

The equation is in standard form.

$$\left(\frac{2\sqrt{3}}{15}+1\right)x=5000$$

Divide both sides by 1+\frac{2}{15}\sqrt{3}.

$$\frac{\left(\frac{2\sqrt{3}}{15}+1\right)x}{\frac{2\sqrt{3}}{15}+1}=\frac{5000}{\frac{2\sqrt{3}}{15}+1}$$

Dividing by 1+\frac{2}{15}\sqrt{3} undoes the multiplication by 1+\frac{2}{15}\sqrt{3}.

$$x=\frac{5000}{\frac{2\sqrt{3}}{15}+1}$$

Divide 5000 by 1+\frac{2}{15}\sqrt{3}.

$$x=\frac{375000-50000\sqrt{3}}{71}$$