Solve 6/3x=8x/2

$$\frac { 6 } { 3 x } = \frac { 8 x } { 2 }$$

Solve for x

$$x=\frac{\sqrt{2}}{2}\approx 0.707106781$$

$$x=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

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 6x, the least common multiple of 3x,2.

$$2\times 6=3x\times 8x$$

Multiply 2 and 6 to get 12.

$$12=3x\times 8x$$

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

$$12=3x^{2}\times 8$$

Multiply 3 and 8 to get 24.

$$12=24x^{2}$$

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

$$24x^{2}=12$$

Divide both sides by 24.

$$x^{2}=\frac{12}{24}$$

Reduce the fraction \frac{12}{24} to lowest terms by extracting and canceling out 12.

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

Take the square root of both sides of the equation.

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

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 6x, the least common multiple of 3x,2.

$$2\times 6=3x\times 8x$$

Multiply 2 and 6 to get 12.

$$12=3x\times 8x$$

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

$$12=3x^{2}\times 8$$

Multiply 3 and 8 to get 24.

$$12=24x^{2}$$

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

$$24x^{2}=12$$

Subtract 12 from both sides.

$$24x^{2}-12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 24 for a, 0 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 24\left(-12\right)}}{2\times 24}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 24\left(-12\right)}}{2\times 24}$$

Multiply -4 times 24.

$$x=\frac{0±\sqrt{-96\left(-12\right)}}{2\times 24}$$

Multiply -96 times -12.

$$x=\frac{0±\sqrt{1152}}{2\times 24}$$

Take the square root of 1152.

$$x=\frac{0±24\sqrt{2}}{2\times 24}$$

Multiply 2 times 24.

$$x=\frac{0±24\sqrt{2}}{48}$$

Now solve the equation x=\frac{0±24\sqrt{2}}{48} when ± is plus.

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

Now solve the equation x=\frac{0±24\sqrt{2}}{48} when ± is minus.

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

The equation is now solved.

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