Solve x^2+(3+a)x-a=0

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

Solve for a

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

$$x\neq 1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3+a by x.

$$x^{2}+3x+ax-a=0$$

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

$$3x+ax-a=-x^{2}$$

Subtract 3x from both sides.

$$ax-a=-x^{2}-3x$$

Combine all terms containing a.

$$\left(x-1\right)a=-x^{2}-3x$$

Divide both sides by x-1.

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

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

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

Solve for x (complex solution)

$$x=\frac{\sqrt{\left(a+1\right)\left(a+9\right)}-a-3}{2}$$

$$x=\frac{-\sqrt{\left(a+1\right)\left(a+9\right)}-a-3}{2}$$

Solve for x

$$x=\frac{\sqrt{\left(a+1\right)\left(a+9\right)}-a-3}{2}$$

$$x=\frac{-\sqrt{\left(a+1\right)\left(a+9\right)}-a-3}{2}\text{, }a\leq -9\text{ or }a\geq -1$$