Solve x/6-3/2x=8/3x

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

Solve for x

$$x=5$$

$$x=-5$$

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 6,2x,3x.

$$xx-3\times 3=2\times 8$$

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

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

Multiply -3 and 3 to get -9.

$$x^{2}-9=2\times 8$$

Multiply 2 and 8 to get 16.

$$x^{2}-9=16$$

Add 9 to both sides.

$$x^{2}=16+9$$

Add 16 and 9 to get 25.

$$x^{2}=25$$

Take the square root of both sides of the equation.

$$x=5 x=-5$$

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

$$xx-3\times 3=2\times 8$$

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

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

Multiply -3 and 3 to get -9.

$$x^{2}-9=2\times 8$$

Multiply 2 and 8 to get 16.

$$x^{2}-9=16$$

Subtract 16 from both sides.

$$x^{2}-9-16=0$$

Subtract 16 from -9 to get -25.

$$x^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-25\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-25\right)}}{2}$$

Multiply -4 times -25.

$$x=\frac{0±\sqrt{100}}{2}$$

Take the square root of 100.

$$x=\frac{0±10}{2}$$

Now solve the equation x=\frac{0±10}{2} when ± is plus. Divide 10 by 2.

$$x=5$$

Now solve the equation x=\frac{0±10}{2} when ± is minus. Divide -10 by 2.

$$x=-5$$

The equation is now solved.

$$x=5 x=-5$$