Solve x^2+2b/2ax+c/a=0

$$x ^ { 2 } + 2 \frac { b } { 2 a } x + \frac { c } { a } = 0$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 2a, the least common multiple of 2a,a.

$$2ax^{2}+2bx+2c=0$$

Subtract 2ax^{2} from both sides. Anything subtracted from zero gives its negation.

$$2bx+2c=-2ax^{2}$$

Subtract 2c from both sides.

$$2bx=-2ax^{2}-2c$$

The equation is in standard form.

$$2xb=-2ax^{2}-2c$$

Divide both sides by 2x.

$$\frac{2xb}{2x}=\frac{-2ax^{2}-2c}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$b=\frac{-2ax^{2}-2c}{2x}$$

Divide -2ax^{2}-2c by 2x.

$$b=-ax-\frac{c}{x}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{bx+c}{x^{2}}\text{, }&\left(c\neq 0\text{ or }b\neq 0\right)\text{ and }\left(b=0\text{ or }x\neq -\frac{c}{b}\right)\text{ and }x\neq 0\text{ and }c\neq -bx\\a\neq 0\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2a, the least common multiple of 2a,a.

$$2ax^{2}+2bx+2c=0$$

Subtract 2bx from both sides. Anything subtracted from zero gives its negation.

$$2ax^{2}+2c=-2bx$$

Subtract 2c from both sides.

$$2ax^{2}=-2bx-2c$$

The equation is in standard form.

$$2x^{2}a=-2bx-2c$$

Divide both sides by 2x^{2}.

$$\frac{2x^{2}a}{2x^{2}}=\frac{-2bx-2c}{2x^{2}}$$

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

$$a=\frac{-2bx-2c}{2x^{2}}$$

Divide -2bx-2c by 2x^{2}.

$$a=-\frac{bx+c}{x^{2}}$$

Variable a cannot be equal to 0.

$$a=-\frac{bx+c}{x^{2}}\text{, }a\neq 0$$

Solve for b

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 2a, the least common multiple of 2a,a.

$$2ax^{2}+2bx+2c=0$$

Subtract 2ax^{2} from both sides. Anything subtracted from zero gives its negation.

$$2bx+2c=-2ax^{2}$$

Subtract 2c from both sides.

$$2bx=-2ax^{2}-2c$$

The equation is in standard form.

$$2xb=-2ax^{2}-2c$$

Divide both sides by 2x.

$$\frac{2xb}{2x}=\frac{-2ax^{2}-2c}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$b=\frac{-2ax^{2}-2c}{2x}$$

Divide -2ax^{2}-2c by 2x.

$$b=-ax-\frac{c}{x}$$