Solve 30/x=2x

$$\frac{ 30 }{ x } =2x$$

Solve for x

$$x=\sqrt{15}\approx 3.872983346$$

$$x=-\sqrt{15}\approx -3.872983346$$

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 x.

$$30=2xx$$

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

$$30=2x^{2}$$

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

$$2x^{2}=30$$

Divide both sides by 2.

$$x^{2}=\frac{30}{2}$$

Divide 30 by 2 to get 15.

$$x^{2}=15$$

Take the square root of both sides of the equation.

$$x=\sqrt{15} x=-\sqrt{15}$$

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 x.

$$30=2xx$$

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

$$30=2x^{2}$$

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

$$2x^{2}=30$$

Subtract 30 from both sides.

$$2x^{2}-30=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-30\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-30\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-30\right)}}{2\times 2}$$

Multiply -8 times -30.

$$x=\frac{0±\sqrt{240}}{2\times 2}$$

Take the square root of 240.

$$x=\frac{0±4\sqrt{15}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{15}}{4}$$

Now solve the equation x=\frac{0±4\sqrt{15}}{4} when ± is plus.

$$x=\sqrt{15}$$

Now solve the equation x=\frac{0±4\sqrt{15}}{4} when ± is minus.

$$x=-\sqrt{15}$$

The equation is now solved.

$$x=\sqrt{15} x=-\sqrt{15}$$