Solve (10-x)(2+sqrt{3})=sqrt{3}x

$$(10-x)(2+ \sqrt{ 3 } )= \sqrt{ 3 } x$$

Solve for x

$$x = \frac{5 {(\sqrt{3} + 1)}}{2} \approx 6.830127019$$

Steps for Solving Linear Equation

Apply the distributive property by multiplying each term of 10-x by each term of 2+\sqrt{3}.

$$20+10\sqrt{3}-2x-x\sqrt{3}=\sqrt{3}x$$

Subtract \sqrt{3}x from both sides.

$$20+10\sqrt{3}-2x-x\sqrt{3}-\sqrt{3}x=0$$

Combine -x\sqrt{3} and -\sqrt{3}x to get -2x\sqrt{3}.

$$20+10\sqrt{3}-2x-2x\sqrt{3}=0$$

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$10\sqrt{3}-2x-2x\sqrt{3}=-20$$

Subtract 10\sqrt{3} from both sides.

$$-2x-2x\sqrt{3}=-20-10\sqrt{3}$$

Combine all terms containing x.

$$\left(-2-2\sqrt{3}\right)x=-20-10\sqrt{3}$$

The equation is in standard form.

$$\left(-2\sqrt{3}-2\right)x=-10\sqrt{3}-20$$

Divide both sides by -2-2\sqrt{3}.

$$\frac{\left(-2\sqrt{3}-2\right)x}{-2\sqrt{3}-2}=\frac{-10\sqrt{3}-20}{-2\sqrt{3}-2}$$

Dividing by -2-2\sqrt{3} undoes the multiplication by -2-2\sqrt{3}.

$$x=\frac{-10\sqrt{3}-20}{-2\sqrt{3}-2}$$

Divide -20-10\sqrt{3} by -2-2\sqrt{3}.

$$x=\frac{5\sqrt{3}+5}{2}$$