Solve y=kx^2+6

$$y = k x ^ { 2 } + 6$$

Solve for k (complex solution)

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

Steps for Solving Linear Equation

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

$$kx^{2}+6=y$$

Subtract 6 from both sides.

$$kx^{2}=y-6$$

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

Solve for k

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

Steps for Solving Linear Equation

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

$$kx^{2}+6=y$$

Subtract 6 from both sides.

$$kx^{2}=y-6$$

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-k^{-\frac{1}{2}}\sqrt{y-6}\text{; }x=k^{-\frac{1}{2}}\sqrt{y-6}\text{, }&k\neq 0\\x\in \mathrm{C}\text{, }&y=6\text{ and }k=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{\frac{y-6}{k}}\text{; }x=-\sqrt{\frac{y-6}{k}}\text{, }&\left(y\geq 6\text{ and }k>0\right)\text{ or }\left(y\leq 6\text{ and }k<0\right)\\x\in \mathrm{R}\text{, }&y=6\text{ and }k=0\end{matrix}\right.$$