Solve 10-x/x=sqrt{3}

$$\frac { 10 - x } { x } = \sqrt { 3 }$$

Solve for x

$$x=5\left(\sqrt{3}-1\right)\approx 3.660254038$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$10-x=x\sqrt{3}$$

Subtract x\sqrt{3} from both sides.

$$10-x-x\sqrt{3}=0$$

Subtract 10 from both sides. Anything subtracted from zero gives its negation.

$$-x-x\sqrt{3}=-10$$

Combine all terms containing x.

$$\left(-1-\sqrt{3}\right)x=-10$$

The equation is in standard form.

$$\left(-\sqrt{3}-1\right)x=-10$$

Divide both sides by -1-\sqrt{3}.

$$\frac{\left(-\sqrt{3}-1\right)x}{-\sqrt{3}-1}=-\frac{10}{-\sqrt{3}-1}$$

Dividing by -1-\sqrt{3} undoes the multiplication by -1-\sqrt{3}.

$$x=-\frac{10}{-\sqrt{3}-1}$$

Divide -10 by -1-\sqrt{3}.

$$x=5\sqrt{3}-5$$