Solve 20=4*6*3/R^2

$$20 = \frac { 4 \cdot 6 \cdot 3 } { R ^ { 2 } }$$

Solve for R

$$R = \frac{3 \sqrt{10}}{5} \approx 1.897366596$$

$$R = -\frac{3 \sqrt{10}}{5} \approx -1.897366596$$

Steps by Finding Square Root

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

$$20R^{2}=4\times 6\times 3$$

Multiply 4 and 6 to get 24.

$$20R^{2}=24\times 3$$

Multiply 24 and 3 to get 72.

$$20R^{2}=72$$

Divide both sides by 20.

$$R^{2}=\frac{72}{20}$$

Reduce the fraction \frac{72}{20} to lowest terms by extracting and canceling out 4.

$$R^{2}=\frac{18}{5}$$

Take the square root of both sides of the equation.

$$R=\frac{3\sqrt{10}}{5} R=-\frac{3\sqrt{10}}{5}$$

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 R^{2}.

$$20R^{2}=4\times 6\times 3$$

Multiply 4 and 6 to get 24.

$$20R^{2}=24\times 3$$

Multiply 24 and 3 to get 72.

$$20R^{2}=72$$

Subtract 72 from both sides.

$$20R^{2}-72=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 0 for b, and -72 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$R=\frac{0±\sqrt{0^{2}-4\times 20\left(-72\right)}}{2\times 20}$$

Square 0.

$$R=\frac{0±\sqrt{-4\times 20\left(-72\right)}}{2\times 20}$$

Multiply -4 times 20.

$$R=\frac{0±\sqrt{-80\left(-72\right)}}{2\times 20}$$

Multiply -80 times -72.

$$R=\frac{0±\sqrt{5760}}{2\times 20}$$

Take the square root of 5760.

$$R=\frac{0±24\sqrt{10}}{2\times 20}$$

Multiply 2 times 20.

$$R=\frac{0±24\sqrt{10}}{40}$$

Now solve the equation R=\frac{0±24\sqrt{10}}{40} when ± is plus.

$$R=\frac{3\sqrt{10}}{5}$$

Now solve the equation R=\frac{0±24\sqrt{10}}{40} when ± is minus.

$$R=-\frac{3\sqrt{10}}{5}$$

The equation is now solved.

$$R=\frac{3\sqrt{10}}{5} R=-\frac{3\sqrt{10}}{5}$$