Solve ax^2+19y=6

$$a x ^ { 2 } + 19 y = 6$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{19y-6}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=\frac{6}{19}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 19y from both sides.

$$ax^{2}=6-19y$$

The equation is in standard form.

$$x^{2}a=6-19y$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{6-19y}{x^{2}}$$

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

$$a=\frac{6-19y}{x^{2}}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{19y-6}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=\frac{6}{19}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 19y from both sides.

$$ax^{2}=6-19y$$

The equation is in standard form.

$$x^{2}a=6-19y$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{6-19y}{x^{2}}$$

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

$$a=\frac{6-19y}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-ia^{-\frac{1}{2}}\sqrt{19y-6}\text{; }x=ia^{-\frac{1}{2}}\sqrt{19y-6}\text{, }&a\neq 0\\x\in \mathrm{C}\text{, }&y=\frac{6}{19}\text{ and }a=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{-\frac{19y-6}{a}}\text{; }x=-\sqrt{-\frac{19y-6}{a}}\text{, }&\left(a>0\text{ and }y\leq \frac{6}{19}\right)\text{ or }\left(y\geq \frac{6}{19}\text{ and }a<0\right)\\x\in \mathrm{R}\text{, }&y=\frac{6}{19}\text{ and }a=0\end{matrix}\right.$$