Solve 2xdiv3/5=2/3*1/x

$$2 x \div \frac { 3 } { 5 } = \frac { 2 } { 3 } \times \frac { 1 } { x }$$

Solve for x

$$x=\frac{\sqrt{5}}{5}\approx 0.447213595$$

$$x=-\frac{\sqrt{5}}{5}\approx -0.447213595$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x, the least common multiple of 3,x.

$$3x\times \frac{2x}{\frac{3}{5}}=\frac{2}{3}\times 3\times 1$$

Divide 2x by \frac{3}{5} to get \frac{10}{3}x.

$$3x\times \frac{10}{3}x=\frac{2}{3}\times 3\times 1$$

Cancel out 3 and 3.

$$10xx=\frac{2}{3}\times 3\times 1$$

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

$$10x^{2}=\frac{2}{3}\times 3\times 1$$

Cancel out 3 and 3.

$$10x^{2}=2\times 1$$

Multiply 2 and 1 to get 2.

$$10x^{2}=2$$

Divide both sides by 10.

$$x^{2}=\frac{2}{10}$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{1}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{5}}{5} x=-\frac{\sqrt{5}}{5}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x, the least common multiple of 3,x.

$$3x\times \frac{2x}{\frac{3}{5}}=\frac{2}{3}\times 3\times 1$$

Divide 2x by \frac{3}{5} to get \frac{10}{3}x.

$$3x\times \frac{10}{3}x=\frac{2}{3}\times 3\times 1$$

Cancel out 3 and 3.

$$10xx=\frac{2}{3}\times 3\times 1$$

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

$$10x^{2}=\frac{2}{3}\times 3\times 1$$

Cancel out 3 and 3.

$$10x^{2}=2\times 1$$

Multiply 2 and 1 to get 2.

$$10x^{2}=2$$

Subtract 2 from both sides.

$$10x^{2}-2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 10\left(-2\right)}}{2\times 10}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 10\left(-2\right)}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{0±\sqrt{-40\left(-2\right)}}{2\times 10}$$

Multiply -40 times -2.

$$x=\frac{0±\sqrt{80}}{2\times 10}$$

Take the square root of 80.

$$x=\frac{0±4\sqrt{5}}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{0±4\sqrt{5}}{20}$$

Now solve the equation x=\frac{0±4\sqrt{5}}{20} when ± is plus.

$$x=\frac{\sqrt{5}}{5}$$

Now solve the equation x=\frac{0±4\sqrt{5}}{20} when ± is minus.

$$x=-\frac{\sqrt{5}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{5}}{5} x=-\frac{\sqrt{5}}{5}$$