Solve ax^2+2by=5

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

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Subtract 2by from both sides.

$$ax^{2}=5-2by$$

The equation is in standard form.

$$x^{2}a=5-2by$$

Divide both sides by x^{2}.

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

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

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

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Subtract ax^{2} from both sides.

$$2by=5-ax^{2}$$

Reorder the terms.

$$2by=-ax^{2}+5$$

The equation is in standard form.

$$2yb=5-ax^{2}$$

Divide both sides by 2y.

$$\frac{2yb}{2y}=\frac{5-ax^{2}}{2y}$$

Dividing by 2y undoes the multiplication by 2y.

$$b=\frac{5-ax^{2}}{2y}$$

Solve for a

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

Steps for Solving Linear Equation

Subtract 2by from both sides.

$$ax^{2}=5-2by$$

The equation is in standard form.

$$x^{2}a=5-2by$$

Divide both sides by x^{2}.

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

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

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

Solve for b

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

Steps for Solving Linear Equation

Subtract ax^{2} from both sides.

$$2by=5-ax^{2}$$

Reorder the terms.

$$2by=-ax^{2}+5$$

The equation is in standard form.

$$2yb=5-ax^{2}$$

Divide both sides by 2y.

$$\frac{2yb}{2y}=\frac{5-ax^{2}}{2y}$$

Dividing by 2y undoes the multiplication by 2y.

$$b=\frac{5-ax^{2}}{2y}$$