Solve 6=R+4R/R*4R

$$6 = \frac { R + 4 R } { R \times 4 R }$$

Solve for R

$$R=\frac{5}{24}\approx 0.208333333$$

Steps Using Factoring

Variable R cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4R^{2}.

$$24R^{2}=R+4R$$

Combine R and 4R to get 5R.

$$24R^{2}=5R$$

Subtract 5R from both sides.

$$24R^{2}-5R=0$$

Factor out R.

$$R\left(24R-5\right)=0$$

To find equation solutions, solve R=0 and 24R-5=0.

$$R=0 R=\frac{5}{24}$$

Variable R cannot be equal to 0.

$$R=\frac{5}{24}$$

Steps Using the Quadratic Formula

Variable R cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4R^{2}.

$$24R^{2}=R+4R$$

Combine R and 4R to get 5R.

$$24R^{2}=5R$$

Subtract 5R from both sides.

$$24R^{2}-5R=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 24 for a, -5 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$R=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}}}{2\times 24}$$

Take the square root of \left(-5\right)^{2}.

$$R=\frac{-\left(-5\right)±5}{2\times 24}$$

The opposite of -5 is 5.

$$R=\frac{5±5}{2\times 24}$$

Multiply 2 times 24.

$$R=\frac{5±5}{48}$$

Now solve the equation R=\frac{5±5}{48} when ± is plus. Add 5 to 5.

$$R=\frac{10}{48}$$

Reduce the fraction \frac{10}{48} to lowest terms by extracting and canceling out 2.

$$R=\frac{5}{24}$$

Now solve the equation R=\frac{5±5}{48} when ± is minus. Subtract 5 from 5.

$$R=\frac{0}{48}$$

Divide 0 by 48.

$$R=0$$

The equation is now solved.

$$R=\frac{5}{24} R=0$$

Variable R cannot be equal to 0.

$$R=\frac{5}{24}$$

Steps for Completing the Square

Variable R cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4R^{2}.

$$24R^{2}=R+4R$$

Combine R and 4R to get 5R.

$$24R^{2}=5R$$

Subtract 5R from both sides.

$$24R^{2}-5R=0$$

Divide both sides by 24.

$$\frac{24R^{2}-5R}{24}=\frac{0}{24}$$

Dividing by 24 undoes the multiplication by 24.

$$R^{2}-\frac{5}{24}R=\frac{0}{24}$$

Divide 0 by 24.

$$R^{2}-\frac{5}{24}R=0$$

Divide -\frac{5}{24}, the coefficient of the x term, by 2 to get -\frac{5}{48}. Then add the square of -\frac{5}{48} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$R^{2}-\frac{5}{24}R+\left(-\frac{5}{48}\right)^{2}=\left(-\frac{5}{48}\right)^{2}$$

Square -\frac{5}{48} by squaring both the numerator and the denominator of the fraction.

$$R^{2}-\frac{5}{24}R+\frac{25}{2304}=\frac{25}{2304}$$

Factor R^{2}-\frac{5}{24}R+\frac{25}{2304}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(R-\frac{5}{48}\right)^{2}=\frac{25}{2304}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(R-\frac{5}{48}\right)^{2}}=\sqrt{\frac{25}{2304}}$$

Simplify.

$$R-\frac{5}{48}=\frac{5}{48} R-\frac{5}{48}=-\frac{5}{48}$$

Add \frac{5}{48} to both sides of the equation.

$$R=\frac{5}{24} R=0$$

Variable R cannot be equal to 0.

$$R=\frac{5}{24}$$