Solve ex^2+(p-3)x+p=0

$$e x ^ { 2 } + ( p - 3 ) x + p = 0$$

Solve for p

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

$$x\neq -1$$

Steps for Solving Linear Equation

Use the distributive property to multiply p-3 by x.

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

Subtract ex^{2} from both sides. Anything subtracted from zero gives its negation.

$$px-3x+p=-ex^{2}$$

Add 3x to both sides.

$$px+p=-ex^{2}+3x$$

Combine all terms containing p.

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

The equation is in standard form.

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

Divide both sides by x+1.

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

Dividing by x+1 undoes the multiplication by x+1.

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

Solve for x (complex solution)

$$x=\frac{\sqrt{p^{2}-4ep-6p+9}-p+3}{2e}$$

$$x=\frac{-\sqrt{p^{2}-4ep-6p+9}-p+3}{2e}$$

Solve for x

$$x=\frac{\sqrt{p^{2}-4ep-6p+9}-p+3}{2e}$$

$$x=\frac{-\sqrt{p^{2}-4ep-6p+9}-p+3}{2e}\text{, }p\geq 2\sqrt{e^{2}+3e}+2e+3\text{ or }p\leq -2\sqrt{e^{2}+3e}+2e+3$$