Solve 10/x=2x/5

$$\frac { 10 } { x } = \frac { 2 x } { 5 }$$

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 5x, the least common multiple of x,5.

$$5\times 10=x\times 2x$$

Multiply 5 and 10 to get 50.

$$50=x\times 2x$$

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

$$50=x^{2}\times 2$$

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

$$x^{2}\times 2=50$$

Divide both sides by 2.

$$x^{2}=\frac{50}{2}$$

Divide 50 by 2 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 5x, the least common multiple of x,5.

$$5\times 10=x\times 2x$$

Multiply 5 and 10 to get 50.

$$50=x\times 2x$$

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

$$50=x^{2}\times 2$$

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

$$x^{2}\times 2=50$$

Subtract 50 from both sides.

$$x^{2}\times 2-50=0$$

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.

$$2x^{2}-50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-50\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-50\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-50\right)}}{2\times 2}$$

Multiply -8 times -50.

$$x=\frac{0±\sqrt{400}}{2\times 2}$$

Take the square root of 400.

$$x=\frac{0±20}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±20}{4}$$

Now solve the equation x=\frac{0±20}{4} when ± is plus. Divide 20 by 4.

$$x=5$$

Now solve the equation x=\frac{0±20}{4} when ± is minus. Divide -20 by 4.

$$x=-5$$

The equation is now solved.

$$x=5 x=-5$$