Solve x-3=18/xquad(b)

$$x - 3 = \frac { 18 } { x } \quad ( b )$$

Solve for b

$$b=\frac{x\left(x-3\right)}{18}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$xx+x\left(-3\right)=18b$$

Multiply x and x to get x^{2}.

$$x^{2}+x\left(-3\right)=18b$$

Swap sides so that all variable terms are on the left hand side.

$$18b=x^{2}+x\left(-3\right)$$

The equation is in standard form.

$$18b=x^{2}-3x$$

Divide both sides by 18.

$$\frac{18b}{18}=\frac{x\left(x-3\right)}{18}$$

Dividing by 18 undoes the multiplication by 18.

$$b=\frac{x\left(x-3\right)}{18}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=\frac{3\sqrt{8b+1}+3}{2}\text{, }&\text{unconditionally}\\x=\frac{-3\sqrt{8b+1}+3}{2}\text{, }&b\neq 0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{-3\sqrt{8b+1}+3}{2}\text{, }&b\neq 0\text{ and }b\geq -\frac{1}{8}\\x=\frac{3\sqrt{8b+1}+3}{2}\text{, }&b\geq -\frac{1}{8}\end{matrix}\right.$$