Solve y=(a+2)x^2+2x-5

$$y = ( a + 2 ) x ^ { 2 } + 2 x - 5$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{5+y-2x-2x^{2}}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=-5\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a+2 by x^{2}.

$$y=ax^{2}+2x^{2}+2x-5$$

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

$$ax^{2}+2x^{2}+2x-5=y$$

Subtract 2x^{2} from both sides.

$$ax^{2}+2x-5=y-2x^{2}$$

Subtract 2x from both sides.

$$ax^{2}-5=y-2x^{2}-2x$$

Add 5 to both sides.

$$ax^{2}=y-2x^{2}-2x+5$$

The equation is in standard form.

$$x^{2}a=5+y-2x-2x^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{5+y-2x-2x^{2}}{x^{2}}$$

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

$$a=\frac{5+y-2x-2x^{2}}{x^{2}}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{5+y-2x-2x^{2}}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=-5\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a+2 by x^{2}.

$$y=ax^{2}+2x^{2}+2x-5$$

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

$$ax^{2}+2x^{2}+2x-5=y$$

Subtract 2x^{2} from both sides.

$$ax^{2}+2x-5=y-2x^{2}$$

Subtract 2x from both sides.

$$ax^{2}-5=y-2x^{2}-2x$$

Add 5 to both sides.

$$ax^{2}=y-2x^{2}-2x+5$$

The equation is in standard form.

$$x^{2}a=5+y-2x-2x^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{5+y-2x-2x^{2}}{x^{2}}$$

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

$$a=\frac{5+y-2x-2x^{2}}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{ay+2y+5a+11}-1}{a+2}\text{; }x=-\frac{\sqrt{ay+2y+5a+11}+1}{a+2}\text{, }&a\neq -2\\x=\frac{y+5}{2}\text{, }&a=-2\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{ay+2y+5a+11}-1}{a+2}\text{; }x=-\frac{\sqrt{ay+2y+5a+11}+1}{a+2}\text{, }&\left(a>-2\text{ or }y\leq -\frac{5a+11}{a+2}\right)\text{ and }\left(y\leq \text{Indeterminate}\text{ or }a\neq -2\right)\text{ and }\left(a<-2\text{ or }\left(a\neq -2\text{ and }y\geq -\frac{5a+11}{a+2}\right)\right)\\x=\frac{y+5}{2}\text{, }&a=-2\end{matrix}\right.$$