Solve y=6-x-x^2a

$$y = 6 - x - x ^ { 2 } a$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{6-y-x}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=6\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$6-x-x^{2}a=y$$

Subtract 6 from both sides.

$$-x-x^{2}a=y-6$$

Add x to both sides.

$$-x^{2}a=y-6+x$$

The equation is in standard form.

$$\left(-x^{2}\right)a=x+y-6$$

Divide both sides by -x^{2}.

$$\frac{\left(-x^{2}\right)a}{-x^{2}}=\frac{x+y-6}{-x^{2}}$$

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

$$a=\frac{x+y-6}{-x^{2}}$$

Divide x-6+y by -x^{2}.

$$a=-\frac{x+y-6}{x^{2}}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{6-y-x}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=6\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$6-x-x^{2}a=y$$

Subtract 6 from both sides.

$$-x-x^{2}a=y-6$$

Add x to both sides.

$$-x^{2}a=y-6+x$$

The equation is in standard form.

$$\left(-x^{2}\right)a=x+y-6$$

Divide both sides by -x^{2}.

$$\frac{\left(-x^{2}\right)a}{-x^{2}}=\frac{x+y-6}{-x^{2}}$$

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

$$a=\frac{x+y-6}{-x^{2}}$$

Divide x-6+y by -x^{2}.

$$a=-\frac{x+y-6}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{1+24a-4ay}+1}{2a}\text{; }x=-\frac{-\sqrt{1+24a-4ay}+1}{2a}\text{, }&a\neq 0\\x=6-y\text{, }&a=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\sqrt{1+24a-4ay}+1}{2a}\text{; }x=-\frac{-\sqrt{1+24a-4ay}+1}{2a}\text{, }&\left(a<0\text{ or }y\leq \frac{24a+1}{4a}\right)\text{ and }\left(y\leq \text{Indeterminate}\text{ or }a\neq 0\right)\text{ and }\left(a>0\text{ or }\left(a\neq 0\text{ and }y\geq \frac{24a+1}{4a}\right)\right)\\x=6-y\text{, }&a=0\end{matrix}\right.$$