Solve 5/3x=3x/8

$$\frac{ 5 }{ 3x } = \frac{ 3x }{ 8 }$$

Solve for x

$$x = -\frac{2 \sqrt{10}}{3} \approx -2.108185107$$

$$x = \frac{2 \sqrt{10}}{3} \approx 2.108185107$$

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 24x, the least common multiple of 3x,8.

$$8\times 5=3x\times 3x$$

Multiply 3x and 3x to get \left(3x\right)^{2}.

$$8\times 5=\left(3x\right)^{2}$$

Multiply 8 and 5 to get 40.

$$40=\left(3x\right)^{2}$$

Expand \left(3x\right)^{2}.

$$40=3^{2}x^{2}$$

Calculate 3 to the power of 2 and get 9.

$$40=9x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$9x^{2}=40$$

Divide both sides by 9.

$$x^{2}=\frac{40}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{10}}{3} x=-\frac{2\sqrt{10}}{3}$$

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 24x, the least common multiple of 3x,8.

$$8\times 5=3x\times 3x$$

Multiply 3x and 3x to get \left(3x\right)^{2}.

$$8\times 5=\left(3x\right)^{2}$$

Multiply 8 and 5 to get 40.

$$40=\left(3x\right)^{2}$$

Expand \left(3x\right)^{2}.

$$40=3^{2}x^{2}$$

Calculate 3 to the power of 2 and get 9.

$$40=9x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$9x^{2}=40$$

Subtract 40 from both sides.

$$9x^{2}-40=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -40 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-40\right)}}{2\times 9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 9\left(-40\right)}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\left(-40\right)}}{2\times 9}$$

Multiply -36 times -40.

$$x=\frac{0±\sqrt{1440}}{2\times 9}$$

Take the square root of 1440.

$$x=\frac{0±12\sqrt{10}}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±12\sqrt{10}}{18}$$

Now solve the equation x=\frac{0±12\sqrt{10}}{18} when ± is plus.

$$x=\frac{2\sqrt{10}}{3}$$

Now solve the equation x=\frac{0±12\sqrt{10}}{18} when ± is minus.

$$x=-\frac{2\sqrt{10}}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{10}}{3} x=-\frac{2\sqrt{10}}{3}$$