Solve 2d/p+4c=sqrt{2x}

$$\frac { 2 d } { p + 4 c } = \sqrt { 2 x }$$

Solve for d

$$d=\frac{\sqrt{2x}\left(p+4c\right)}{2}$$

$$x\geq 0\text{ and }p\neq -4c$$

Steps for Solving Linear Equation

Multiply both sides of the equation by p+4c.

$$2d=\left(p+4c\right)\sqrt{2x}$$

Use the distributive property to multiply p+4c by \sqrt{2x}.

$$2d=p\sqrt{2x}+4c\sqrt{2x}$$

The equation is in standard form.

$$2d=\sqrt{2x}p+4\sqrt{2x}c$$

Divide both sides by 2.

$$\frac{2d}{2}=\frac{\sqrt{2x}\left(p+4c\right)}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$d=\frac{\sqrt{2x}\left(p+4c\right)}{2}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{-p+\sqrt{\frac{2}{x}}d}{4}\text{, }&d\neq 0\text{ and }x>0\\c\neq -\frac{p}{4}\text{, }&d=0\text{ and }x=0\end{matrix}\right.$$