Solve 2t/5sqrt{3}=frac{5sqrt{3}-sqrt{3}t}{10}

$$\frac { 2 t } { 5 \sqrt { 3 } } = \frac { 5 \sqrt { 3 } - \sqrt { 3 } t } { 10 }$$

Solve for t

$$t = \frac{15}{7} = 2\frac{1}{7} \approx 2.142857143$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10.

$$\frac{2}{3}\times 3^{\frac{1}{2}}\times 2t=5\sqrt{3}-\sqrt{3}t$$

Express \frac{2}{3}\times 2 as a single fraction.

$$\frac{2\times 2}{3}\times 3^{\frac{1}{2}}t=5\sqrt{3}-\sqrt{3}t$$

Multiply 2 and 2 to get 4.

$$\frac{4}{3}\times 3^{\frac{1}{2}}t=5\sqrt{3}-\sqrt{3}t$$

Add \sqrt{3}t to both sides.

$$\frac{4}{3}\times 3^{\frac{1}{2}}t+\sqrt{3}t=5\sqrt{3}$$

Reorder the terms.

$$\frac{4}{3}\sqrt{3}t+\sqrt{3}t=5\sqrt{3}$$

Combine \frac{4}{3}\sqrt{3}t and \sqrt{3}t to get \frac{7}{3}\sqrt{3}t.

$$\frac{7}{3}\sqrt{3}t=5\sqrt{3}$$

The equation is in standard form.

$$\frac{7\sqrt{3}}{3}t=5\sqrt{3}$$

Divide both sides by \frac{7}{3}\sqrt{3}.

$$\frac{3\times \frac{7\sqrt{3}}{3}t}{7\sqrt{3}}=\frac{3\times 5\sqrt{3}}{7\sqrt{3}}$$

Dividing by \frac{7}{3}\sqrt{3} undoes the multiplication by \frac{7}{3}\sqrt{3}.

$$t=\frac{3\times 5\sqrt{3}}{7\sqrt{3}}$$

Divide 5\sqrt{3} by \frac{7}{3}\sqrt{3}.

$$t=\frac{15}{7}$$