Solve 20/r+xsqrt{x}+x=22

$$\frac { 20 } { r } + x \sqrt { x } + x = 22$$

Solve for r

$$r=-\frac{20}{x^{\frac{3}{2}}+x-22}$$

$$x\neq \frac{\sqrt[3]{66\sqrt{9735}+6337}+\sqrt[3]{6337-66\sqrt{9735}}+1}{3}\text{ and }x\geq 0$$

Steps for Solving Linear Equation

Variable r cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by r.

$$20+x\sqrt{x}r+rx=22r$$

Subtract 22r from both sides.

$$20+x\sqrt{x}r+rx-22r=0$$

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$x\sqrt{x}r+rx-22r=-20$$

Combine all terms containing r.

$$\left(x\sqrt{x}+x-22\right)r=-20$$

The equation is in standard form.

$$\left(\sqrt{x}x+x-22\right)r=-20$$

Divide both sides by x\sqrt{x}+x-22.

$$\frac{\left(\sqrt{x}x+x-22\right)r}{\sqrt{x}x+x-22}=-\frac{20}{\sqrt{x}x+x-22}$$

Dividing by x\sqrt{x}+x-22 undoes the multiplication by x\sqrt{x}+x-22.

$$r=-\frac{20}{\sqrt{x}x+x-22}$$

Divide -20 by x\sqrt{x}+x-22.

$$r=-\frac{20}{x^{\frac{3}{2}}+x-22}$$

Variable r cannot be equal to 0.

$$r=-\frac{20}{x^{\frac{3}{2}}+x-22}\text{, }r\neq 0$$