Solve r/4=h+8e/h/3

$$\frac { r } { 4 } = \frac { h + 8 \frac { e } { h } } { 3 }$$

Solve for r

$$r=\frac{4h}{3}+\frac{32e}{3h}$$

$$h\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,3.

$$3r=4\left(h+8\times \frac{e}{h}\right)$$

Express 8\times \frac{e}{h} as a single fraction.

$$3r=4\left(h+\frac{8e}{h}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply h times \frac{h}{h}.

$$3r=4\left(\frac{hh}{h}+\frac{8e}{h}\right)$$

Since \frac{hh}{h} and \frac{8e}{h} have the same denominator, add them by adding their numerators.

$$3r=4\times \frac{hh+8e}{h}$$

Do the multiplications in hh+8e.

$$3r=4\times \frac{h^{2}+8e}{h}$$

Express 4\times \frac{h^{2}+8e}{h} as a single fraction.

$$3r=\frac{4\left(h^{2}+8e\right)}{h}$$

Use the distributive property to multiply 4 by h^{2}+8e.

$$3r=\frac{4h^{2}+32e}{h}$$

Multiply both sides of the equation by h.

$$3rh=4h^{2}+32e$$

The equation is in standard form.

$$3hr=4h^{2}+32e$$

Divide both sides by 3h.

$$\frac{3hr}{3h}=\frac{4h^{2}+32e}{3h}$$

Dividing by 3h undoes the multiplication by 3h.

$$r=\frac{4h^{2}+32e}{3h}$$

Divide 4h^{2}+32e by 3h.

$$r=\frac{4h}{3}+\frac{32e}{3h}$$

Solve for h (complex solution)

$$h=\frac{\sqrt{9r^{2}-512e}+3r}{8}$$

$$h=\frac{-\sqrt{9r^{2}-512e}+3r}{8}$$

Solve for h

$$h=\frac{\sqrt{9r^{2}-512e}+3r}{8}$$

$$h=\frac{-\sqrt{9r^{2}-512e}+3r}{8}\text{, }|r|\geq \frac{16\sqrt{2e}}{3}$$