Solve D^218=-4/2s(20)+b=

$$D ^ { 2 } 18 = - \frac { 4 } { 2 s } ( 20 ) + b =$$

Solve for b

$$b=18D^{2}+\frac{40}{s}$$

$$s\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2s.

$$D^{2}\times 18\times 2s=\left(-\frac{4}{2s}\right)\times 20\times 2s+2sb$$

Multiply 18 and 2 to get 36.

$$D^{2}\times 36s=\left(-\frac{4}{2s}\right)\times 20\times 2s+2sb$$

Multiply 20 and 2 to get 40.

$$D^{2}\times 36s=\left(-\frac{4}{2s}\right)\times 40s+2sb$$

Express \left(-\frac{4}{2s}\right)\times 40 as a single fraction.

$$D^{2}\times 36s=\frac{-4\times 40}{2s}s+2sb$$

Cancel out 2 in both numerator and denominator.

$$D^{2}\times 36s=\frac{-2\times 40}{s}s+2sb$$

Express \frac{-2\times 40}{s}s as a single fraction.

$$D^{2}\times 36s=\frac{-2\times 40s}{s}+2sb$$

Cancel out s in both numerator and denominator.

$$D^{2}\times 36s=-2\times 40+2sb$$

Multiply -2 and 40 to get -80.

$$D^{2}\times 36s=-80+2sb$$

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

$$-80+2sb=D^{2}\times 36s$$

Add 80 to both sides.

$$2sb=D^{2}\times 36s+80$$

The equation is in standard form.

$$2sb=36sD^{2}+80$$

Divide both sides by 2s.

$$\frac{2sb}{2s}=\frac{36sD^{2}+80}{2s}$$

Dividing by 2s undoes the multiplication by 2s.

$$b=\frac{36sD^{2}+80}{2s}$$

Divide 36D^{2}s+80 by 2s.

$$b=18D^{2}+\frac{40}{s}$$

Solve for D (complex solution)

$$D=-\frac{\sqrt{2b-\frac{80}{s}}}{6}$$

$$D=\frac{\sqrt{2b-\frac{80}{s}}}{6}\text{, }s\neq 0$$

Solve for D

$$D=\frac{\sqrt{2b-\frac{80}{s}}}{6}$$

$$D=-\frac{\sqrt{2b-\frac{80}{s}}}{6}\text{, }\left(b\geq 0\text{ and }s<0\right)\text{ or }\left(s\geq \frac{40}{b}\text{ and }b>0\text{ and }s\neq 0\right)\text{ or }\left(s\geq \frac{40}{b}\text{ and }s<0\right)$$