Solve frac{5sqrt{7}}{14}x=frac{2sqrt{7}}{7}(sqrt{21}-x)

$$\frac { 5 \sqrt { 7 } } { 14 } x = \frac { 2 \sqrt { 7 } } { 7 } ( \sqrt { 21 } - x )$$

Solve for x

$$x = \frac{4 \sqrt{21}}{9} \approx 2.036700309$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 14, the least common multiple of 14,7.

$$5\sqrt{7}x=2\times 2\sqrt{7}\left(\sqrt{21}-x\right)$$

Multiply 2 and 2 to get 4.

$$5\sqrt{7}x=4\sqrt{7}\left(\sqrt{21}-x\right)$$

Use the distributive property to multiply 4\sqrt{7} by \sqrt{21}-x.

$$5\sqrt{7}x=4\sqrt{7}\sqrt{21}-4\sqrt{7}x$$

Factor 21=7\times 3. Rewrite the square root of the product \sqrt{7\times 3} as the product of square roots \sqrt{7}\sqrt{3}.

$$5\sqrt{7}x=4\sqrt{7}\sqrt{7}\sqrt{3}-4\sqrt{7}x$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$5\sqrt{7}x=4\times 7\sqrt{3}-4\sqrt{7}x$$

Multiply 4 and 7 to get 28.

$$5\sqrt{7}x=28\sqrt{3}-4\sqrt{7}x$$

Add 4\sqrt{7}x to both sides.

$$5\sqrt{7}x+4\sqrt{7}x=28\sqrt{3}$$

Combine 5\sqrt{7}x and 4\sqrt{7}x to get 9\sqrt{7}x.

$$9\sqrt{7}x=28\sqrt{3}$$

Divide both sides by 9\sqrt{7}.

$$\frac{9\sqrt{7}x}{9\sqrt{7}}=\frac{28\sqrt{3}}{9\sqrt{7}}$$

Dividing by 9\sqrt{7} undoes the multiplication by 9\sqrt{7}.

$$x=\frac{28\sqrt{3}}{9\sqrt{7}}$$

Divide 28\sqrt{3} by 9\sqrt{7}.

$$x=\frac{4\sqrt{21}}{9}$$