Solve 125x/6=4/3piR^3

$$\frac { 125 x } { 6 } = \frac { 4 } { 3 } \pi R ^ { 3 }$$

Solve for x

$$x=\frac{8\pi R^{3}}{125}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 6,3.

$$125x=8\pi R^{3}$$

Divide both sides by 125.

$$\frac{125x}{125}=\frac{8\pi R^{3}}{125}$$

Dividing by 125 undoes the multiplication by 125.

$$x=\frac{8\pi R^{3}}{125}$$

Solve for R (complex solution)

$$R=\frac{5e^{\frac{2\pi i}{3}}\sqrt[3]{\frac{x}{\pi }}}{2}$$

$$R=\frac{5\sqrt[3]{\frac{x}{\pi }}}{2}$$

$$R=\frac{5e^{\frac{4\pi i}{3}}\sqrt[3]{\frac{x}{\pi }}}{2}$$

Solve for R

$$R=\frac{5\sqrt[3]{\frac{x}{\pi }}}{2}$$