Solve 5x/x^2=12

$$\frac{ 5x }{ { x }^{ 2 } } = 12$$

Solve for x

$$x=\frac{5}{12}\approx 0.416666667$$

Steps Using Factoring

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$5x=12x^{2}$$

Subtract 12x^{2} from both sides.

$$5x-12x^{2}=0$$

Factor out x.

$$x\left(5-12x\right)=0$$

To find equation solutions, solve x=0 and 5-12x=0.

$$x=0 x=\frac{5}{12}$$

Variable x cannot be equal to 0.

$$x=\frac{5}{12}$$

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^{2}.

$$5x=12x^{2}$$

Subtract 12x^{2} from both sides.

$$5x-12x^{2}=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$-12x^{2}+5x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -12 for a, 5 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}}}{2\left(-12\right)}$$

Take the square root of 5^{2}.

$$x=\frac{-5±5}{2\left(-12\right)}$$

Multiply 2 times -12.

$$x=\frac{-5±5}{-24}$$

Now solve the equation x=\frac{-5±5}{-24} when ± is plus. Add -5 to 5.

$$x=\frac{0}{-24}$$

Divide 0 by -24.

$$x=0$$

Now solve the equation x=\frac{-5±5}{-24} when ± is minus. Subtract 5 from -5.

$$x=-\frac{10}{-24}$$

Reduce the fraction \frac{-10}{-24} to lowest terms by extracting and canceling out 2.

$$x=\frac{5}{12}$$

The equation is now solved.

$$x=0 x=\frac{5}{12}$$

Variable x cannot be equal to 0.

$$x=\frac{5}{12}$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$5x=12x^{2}$$

Subtract 12x^{2} from both sides.

$$5x-12x^{2}=0$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-12x^{2}+5x=0$$

Divide both sides by -12.

$$\frac{-12x^{2}+5x}{-12}=\frac{0}{-12}$$

Dividing by -12 undoes the multiplication by -12.

$$x^{2}+\frac{5}{-12}x=\frac{0}{-12}$$

Divide 5 by -12.

$$x^{2}-\frac{5}{12}x=\frac{0}{-12}$$

Divide 0 by -12.

$$x^{2}-\frac{5}{12}x=0$$

Divide -\frac{5}{12}, the coefficient of the x term, by 2 to get -\frac{5}{24}. Then add the square of -\frac{5}{24} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{5}{12}x+\left(-\frac{5}{24}\right)^{2}=\left(-\frac{5}{24}\right)^{2}$$

Square -\frac{5}{24} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{5}{12}x+\frac{25}{576}=\frac{25}{576}$$

Factor x^{2}-\frac{5}{12}x+\frac{25}{576}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{5}{24}\right)^{2}=\frac{25}{576}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{5}{24}\right)^{2}}=\sqrt{\frac{25}{576}}$$

Simplify.

$$x-\frac{5}{24}=\frac{5}{24} x-\frac{5}{24}=-\frac{5}{24}$$

Add \frac{5}{24} to both sides of the equation.

$$x=\frac{5}{12} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{5}{12}$$