Solve x^2=2P(sqrt{3}x+b)

$$x ^ { 2 } = 2 P ( \sqrt { 3 } x + b )$$

Solve for P (complex solution)

$$\left\{\begin{matrix}P=\frac{x^{2}}{2\left(\sqrt{3}x+b\right)}\text{, }&x\neq -\frac{\sqrt{3}b}{3}\\P\in \mathrm{C}\text{, }&x=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2P by \sqrt{3}x+b.

$$x^{2}=2P\sqrt{3}x+2Pb$$

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

$$2P\sqrt{3}x+2Pb=x^{2}$$

Combine all terms containing P.

$$\left(2\sqrt{3}x+2b\right)P=x^{2}$$

Divide both sides by 2\sqrt{3}x+2b.

$$\frac{\left(2\sqrt{3}x+2b\right)P}{2\sqrt{3}x+2b}=\frac{x^{2}}{2\sqrt{3}x+2b}$$

Dividing by 2\sqrt{3}x+2b undoes the multiplication by 2\sqrt{3}x+2b.

$$P=\frac{x^{2}}{2\sqrt{3}x+2b}$$

Divide x^{2} by 2\sqrt{3}x+2b.

$$P=\frac{x^{2}}{2\left(\sqrt{3}x+b\right)}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{x\left(-2\sqrt{3}P+x\right)}{2P}\text{, }&P\neq 0\\b\in \mathrm{C}\text{, }&x=0\text{ and }P=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2P by \sqrt{3}x+b.

$$x^{2}=2P\sqrt{3}x+2Pb$$

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

$$2P\sqrt{3}x+2Pb=x^{2}$$

Subtract 2P\sqrt{3}x from both sides.

$$2Pb=x^{2}-2P\sqrt{3}x$$

The equation is in standard form.

$$2Pb=-2\sqrt{3}Px+x^{2}$$

Divide both sides by 2P.

$$\frac{2Pb}{2P}=\frac{x\left(-2\sqrt{3}P+x\right)}{2P}$$

Dividing by 2P undoes the multiplication by 2P.

$$b=\frac{x\left(-2\sqrt{3}P+x\right)}{2P}$$

Solve for P

$$\left\{\begin{matrix}P=\frac{x^{2}}{2\left(\sqrt{3}x+b\right)}\text{, }&x\neq -\frac{\sqrt{3}b}{3}\\P\in \mathrm{R}\text{, }&x=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2P by \sqrt{3}x+b.

$$x^{2}=2P\sqrt{3}x+2Pb$$

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

$$2P\sqrt{3}x+2Pb=x^{2}$$

Combine all terms containing P.

$$\left(2\sqrt{3}x+2b\right)P=x^{2}$$

Divide both sides by 2\sqrt{3}x+2b.

$$\frac{\left(2\sqrt{3}x+2b\right)P}{2\sqrt{3}x+2b}=\frac{x^{2}}{2\sqrt{3}x+2b}$$

Dividing by 2\sqrt{3}x+2b undoes the multiplication by 2\sqrt{3}x+2b.

$$P=\frac{x^{2}}{2\sqrt{3}x+2b}$$

Divide x^{2} by 2\sqrt{3}x+2b.

$$P=\frac{x^{2}}{2\left(\sqrt{3}x+b\right)}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{x\left(-2\sqrt{3}P+x\right)}{2P}\text{, }&P\neq 0\\b\in \mathrm{R}\text{, }&x=0\text{ and }P=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2P by \sqrt{3}x+b.

$$x^{2}=2P\sqrt{3}x+2Pb$$

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

$$2P\sqrt{3}x+2Pb=x^{2}$$

Subtract 2P\sqrt{3}x from both sides.

$$2Pb=x^{2}-2P\sqrt{3}x$$

The equation is in standard form.

$$2Pb=-2\sqrt{3}Px+x^{2}$$

Divide both sides by 2P.

$$\frac{2Pb}{2P}=\frac{x\left(-2\sqrt{3}P+x\right)}{2P}$$

Dividing by 2P undoes the multiplication by 2P.

$$b=\frac{x\left(-2\sqrt{3}P+x\right)}{2P}$$