Solve 5/x=4x/5

$$\frac { 5 } { x } = \frac { 4 x } { 5 }$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

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.

$$5\times 5=x\times 4x$$

Multiply 5 and 5 to get 25.

$$25=x\times 4x$$

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

$$25=x^{2}\times 4$$

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

$$x^{2}\times 4=25$$

Divide both sides by 4.

$$x^{2}=\frac{25}{4}$$

Take the square root of both sides of the equation.

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

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.

$$5\times 5=x\times 4x$$

Multiply 5 and 5 to get 25.

$$25=x\times 4x$$

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

$$25=x^{2}\times 4$$

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

$$x^{2}\times 4=25$$

Subtract 25 from both sides.

$$x^{2}\times 4-25=0$$

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.

$$4x^{2}-25=0$$

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

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

Square 0.

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

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-25\right)}}{2\times 4}$$

Multiply -16 times -25.

$$x=\frac{0±\sqrt{400}}{2\times 4}$$

Take the square root of 400.

$$x=\frac{0±20}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±20}{8}$$

Now solve the equation x=\frac{0±20}{8} when ± is plus. Reduce the fraction \frac{20}{8} to lowest terms by extracting and canceling out 4.

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

Now solve the equation x=\frac{0±20}{8} when ± is minus. Reduce the fraction \frac{-20}{8} to lowest terms by extracting and canceling out 4.

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

The equation is now solved.

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