Solve (sqrt{5}x-2)*frac{2sqrt{3}}{3}=2x

$$( \sqrt { 5 } x - 2 ) \times \frac { 2 \sqrt { 3 } } { 3 } = 2 x$$

Solve for x

$$x=\sqrt{3}+\sqrt{5}\approx 3.968118785$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$\left(\sqrt{5}x-2\right)\times 2\sqrt{3}=6x$$

Use the distributive property to multiply \sqrt{5}x-2 by 2.

$$\left(2\sqrt{5}x-4\right)\sqrt{3}=6x$$

Use the distributive property to multiply 2\sqrt{5}x-4 by \sqrt{3}.

$$2\sqrt{5}x\sqrt{3}-4\sqrt{3}=6x$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$2\sqrt{15}x-4\sqrt{3}=6x$$

Subtract 6x from both sides.

$$2\sqrt{15}x-4\sqrt{3}-6x=0$$

Add 4\sqrt{3} to both sides. Anything plus zero gives itself.

$$2\sqrt{15}x-6x=4\sqrt{3}$$

Combine all terms containing x.

$$\left(2\sqrt{15}-6\right)x=4\sqrt{3}$$

Divide both sides by 2\sqrt{15}-6.

$$\frac{\left(2\sqrt{15}-6\right)x}{2\sqrt{15}-6}=\frac{4\sqrt{3}}{2\sqrt{15}-6}$$

Dividing by 2\sqrt{15}-6 undoes the multiplication by 2\sqrt{15}-6.

$$x=\frac{4\sqrt{3}}{2\sqrt{15}-6}$$

Divide 4\sqrt{3} by 2\sqrt{15}-6.

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