Solve 100/133(130-x)=sqrt{3}(90-x)

$$\frac{ 100 }{ 133 } (130-x)= \sqrt{ 3 } (90-x)$$

Solve for x

$$x = \frac{3476030 - 532000 \sqrt{3}}{43067} \approx 59.316390052$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{100}{133} by 130-x.

$$\frac{100}{133}\times 130+\frac{100}{133}\left(-1\right)x=\sqrt{3}\left(90-x\right)$$

Express \frac{100}{133}\times 130 as a single fraction.

$$\frac{100\times 130}{133}+\frac{100}{133}\left(-1\right)x=\sqrt{3}\left(90-x\right)$$

Multiply 100 and 130 to get 13000.

$$\frac{13000}{133}+\frac{100}{133}\left(-1\right)x=\sqrt{3}\left(90-x\right)$$

Multiply \frac{100}{133} and -1 to get -\frac{100}{133}.

$$\frac{13000}{133}-\frac{100}{133}x=\sqrt{3}\left(90-x\right)$$

Use the distributive property to multiply \sqrt{3} by 90-x.

$$\frac{13000}{133}-\frac{100}{133}x=90\sqrt{3}-\sqrt{3}x$$

Add \sqrt{3}x to both sides.

$$\frac{13000}{133}-\frac{100}{133}x+\sqrt{3}x=90\sqrt{3}$$

Subtract \frac{13000}{133} from both sides.

$$-\frac{100}{133}x+\sqrt{3}x=90\sqrt{3}-\frac{13000}{133}$$

Combine all terms containing x.

$$\left(-\frac{100}{133}+\sqrt{3}\right)x=90\sqrt{3}-\frac{13000}{133}$$

The equation is in standard form.

$$\left(\sqrt{3}-\frac{100}{133}\right)x=90\sqrt{3}-\frac{13000}{133}$$

Divide both sides by -\frac{100}{133}+\sqrt{3}.

$$\frac{\left(\sqrt{3}-\frac{100}{133}\right)x}{\sqrt{3}-\frac{100}{133}}=\frac{90\sqrt{3}-\frac{13000}{133}}{\sqrt{3}-\frac{100}{133}}$$

Dividing by -\frac{100}{133}+\sqrt{3} undoes the multiplication by -\frac{100}{133}+\sqrt{3}.

$$x=\frac{90\sqrt{3}-\frac{13000}{133}}{\sqrt{3}-\frac{100}{133}}$$

Divide 90\sqrt{3}-\frac{13000}{133} by -\frac{100}{133}+\sqrt{3}.

$$x=\frac{3476030-532000\sqrt{3}}{43067}$$