Solve px^2-p+10=2px+4x

$$p x ^ { 2 } - p + 10 = 2 p x + 4 x$$

Solve for p

$$p=-\frac{2\left(5-2x\right)}{x^{2}-2x-1}$$

$$x\neq \sqrt{2}+1\text{ and }x\neq 1-\sqrt{2}$$

Steps for Solving Linear Equation

Subtract 2px from both sides.

$$px^{2}-p+10-2px=4x$$

Subtract 10 from both sides.

$$px^{2}-p-2px=4x-10$$

Combine all terms containing p.

$$\left(x^{2}-1-2x\right)p=4x-10$$

The equation is in standard form.

$$\left(x^{2}-2x-1\right)p=4x-10$$

Divide both sides by x^{2}-2x-1.

$$\frac{\left(x^{2}-2x-1\right)p}{x^{2}-2x-1}=\frac{4x-10}{x^{2}-2x-1}$$

Dividing by x^{2}-2x-1 undoes the multiplication by x^{2}-2x-1.

$$p=\frac{4x-10}{x^{2}-2x-1}$$

Divide 4x-10 by x^{2}-2x-1.

$$p=\frac{2\left(2x-5\right)}{x^{2}-2x-1}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{2\left(p-2\right)\left(p-1\right)}+p+2}{p}\text{; }x=\frac{-\sqrt{2\left(p-2\right)\left(p-1\right)}+p+2}{p}\text{, }&p\neq 0\\x=\frac{5}{2}\text{, }&p=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{2\left(p-2\right)\left(p-1\right)}+p+2}{p}\text{; }x=\frac{-\sqrt{2\left(p-2\right)\left(p-1\right)}+p+2}{p}\text{, }&p\geq 2\text{ or }\left(p\neq 0\text{ and }p\leq 1\right)\\x=\frac{5}{2}\text{, }&p=0\end{matrix}\right.$$