Solve 2x/2=6/x

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

Solve for x

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

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

$$x\times 2x=2\times 6$$

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

$$x^{2}\times 2=2\times 6$$

Multiply 2 and 6 to get 12.

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

Divide both sides by 2.

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

Divide 12 by 2 to get 6.

$$x^{2}=6$$

Take the square root of both sides of the equation.

$$x=\sqrt{6} x=-\sqrt{6}$$

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

$$x\times 2x=2\times 6$$

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

$$x^{2}\times 2=2\times 6$$

Multiply 2 and 6 to get 12.

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

Subtract 12 from both sides.

$$x^{2}\times 2-12=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

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

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

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

Square 0.

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

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-12\right)}}{2\times 2}$$

Multiply -8 times -12.

$$x=\frac{0±\sqrt{96}}{2\times 2}$$

Take the square root of 96.

$$x=\frac{0±4\sqrt{6}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{6}}{4}$$

Now solve the equation x=\frac{0±4\sqrt{6}}{4} when ± is plus.

$$x=\sqrt{6}$$

Now solve the equation x=\frac{0±4\sqrt{6}}{4} when ± is minus.

$$x=-\sqrt{6}$$

The equation is now solved.

$$x=\sqrt{6} x=-\sqrt{6}$$