Solve px^2-3px+p+5=0

$$p x ^ { 2 } - 3 p x + p + 5 = 0$$

Solve for p

$$p=-\frac{5}{x^{2}-3x+1}$$

$$x\neq \frac{\sqrt{5}+3}{2}\text{ and }x\neq \frac{3-\sqrt{5}}{2}$$

Steps for Solving Linear Equation

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$px^{2}-3px+p=-5$$

Combine all terms containing p.

$$\left(x^{2}-3x+1\right)p=-5$$

Divide both sides by x^{2}-3x+1.

$$\frac{\left(x^{2}-3x+1\right)p}{x^{2}-3x+1}=-\frac{5}{x^{2}-3x+1}$$

Dividing by x^{2}-3x+1 undoes the multiplication by x^{2}-3x+1.

$$p=-\frac{5}{x^{2}-3x+1}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{5p^{2}-20p}}{2p}+\frac{3}{2}$$

$$x=-\frac{\sqrt{5p^{2}-20p}}{2p}+\frac{3}{2}\text{, }p\neq 0$$

Solve for x

$$x=\frac{\sqrt{5p^{2}-20p}}{2p}+\frac{3}{2}$$

$$x=-\frac{\sqrt{5p^{2}-20p}}{2p}+\frac{3}{2}\text{, }p<0\text{ or }p\geq 4$$