Solve 18/x=2x/4

$$\frac { 18 } { x } = \frac { 2 x } { 4 }$$

Solve for x

$$x=6$$

$$x=-6$$

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 4x, the least common multiple of x,4.

$$4\times 18=x\times 2x$$

Multiply 4 and 18 to get 72.

$$72=x\times 2x$$

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

$$72=x^{2}\times 2$$

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

$$x^{2}\times 2=72$$

Divide both sides by 2.

$$x^{2}=\frac{72}{2}$$

Divide 72 by 2 to get 36.

$$x^{2}=36$$

Take the square root of both sides of the equation.

$$x=6 x=-6$$

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 4x, the least common multiple of x,4.

$$4\times 18=x\times 2x$$

Multiply 4 and 18 to get 72.

$$72=x\times 2x$$

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

$$72=x^{2}\times 2$$

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

$$x^{2}\times 2=72$$

Subtract 72 from both sides.

$$x^{2}\times 2-72=0$$

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.

$$2x^{2}-72=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -72 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-72\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-72\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-72\right)}}{2\times 2}$$

Multiply -8 times -72.

$$x=\frac{0±\sqrt{576}}{2\times 2}$$

Take the square root of 576.

$$x=\frac{0±24}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±24}{4}$$

Now solve the equation x=\frac{0±24}{4} when ± is plus. Divide 24 by 4.

$$x=6$$

Now solve the equation x=\frac{0±24}{4} when ± is minus. Divide -24 by 4.

$$x=-6$$

The equation is now solved.

$$x=6 x=-6$$