Solve 2/3/frac{7{3}a}=-3a/frac{7{3}}

$$\frac { \frac { 2 } { 3 } } { \frac { 7 } { 3 } a } = \frac { - 3 a } { \frac { 7 } { 3 } }$$

Solve for a

$$a=-\frac{\sqrt{2}i}{3}\approx -0-0.471404521i$$

$$a=\frac{\sqrt{2}i}{3}\approx 0.471404521i$$

Steps by Finding Square Root

Express \frac{\frac{2}{3}}{\frac{7}{3}a} as a single fraction.

$$\frac{2}{3\times \frac{7}{3}a}=\frac{-3a}{\frac{7}{3}}$$

Multiply 3 and \frac{7}{3} to get 7.

$$\frac{2}{7a}=\frac{-3a}{\frac{7}{3}}$$

Divide -3a by \frac{7}{3} to get -\frac{9}{7}a.

$$\frac{2}{7a}=-\frac{9}{7}a$$

Add \frac{9}{7}a to both sides.

$$\frac{2}{7a}+\frac{9}{7}a=0$$

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 7a, the least common multiple of 7a,7.

$$2+\frac{9}{7}a\times 7a=0$$

Reorder the terms.

$$\frac{9}{7}\times 7aa+2=0$$

Multiply a and a to get a^{2}.

$$\frac{9}{7}\times 7a^{2}+2=0$$

Multiply \frac{9}{7} and 7 to get 9.

$$9a^{2}+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$9a^{2}=-2$$

Divide both sides by 9.

$$a^{2}=-\frac{2}{9}$$

The equation is now solved.

$$a=\frac{\sqrt{2}i}{3} a=-\frac{\sqrt{2}i}{3}$$

Steps Using the Quadratic Formula

Express \frac{\frac{2}{3}}{\frac{7}{3}a} as a single fraction.

$$\frac{2}{3\times \frac{7}{3}a}=\frac{-3a}{\frac{7}{3}}$$

Multiply 3 and \frac{7}{3} to get 7.

$$\frac{2}{7a}=\frac{-3a}{\frac{7}{3}}$$

Divide -3a by \frac{7}{3} to get -\frac{9}{7}a.

$$\frac{2}{7a}=-\frac{9}{7}a$$

Add \frac{9}{7}a to both sides.

$$\frac{2}{7a}+\frac{9}{7}a=0$$

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 7a, the least common multiple of 7a,7.

$$2+\frac{9}{7}a\times 7a=0$$

Reorder the terms.

$$\frac{9}{7}\times 7aa+2=0$$

Multiply a and a to get a^{2}.

$$\frac{9}{7}\times 7a^{2}+2=0$$

Multiply \frac{9}{7} and 7 to get 9.

$$9a^{2}+2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and 2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 9\times 2}}{2\times 9}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 9\times 2}}{2\times 9}$$

Multiply -4 times 9.

$$a=\frac{0±\sqrt{-36\times 2}}{2\times 9}$$

Multiply -36 times 2.

$$a=\frac{0±\sqrt{-72}}{2\times 9}$$

Take the square root of -72.

$$a=\frac{0±6\sqrt{2}i}{2\times 9}$$

Multiply 2 times 9.

$$a=\frac{0±6\sqrt{2}i}{18}$$

Now solve the equation a=\frac{0±6\sqrt{2}i}{18} when ± is plus.

$$a=\frac{\sqrt{2}i}{3}$$

Now solve the equation a=\frac{0±6\sqrt{2}i}{18} when ± is minus.

$$a=-\frac{\sqrt{2}i}{3}$$

The equation is now solved.

$$a=\frac{\sqrt{2}i}{3} a=-\frac{\sqrt{2}i}{3}$$