Solve ax^2+b+c=0

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

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Subtract b from both sides. Anything subtracted from zero gives its negation.

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

Subtract c from both sides.

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

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

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

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

Solve for a

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

Steps for Solving Linear Equation

Subtract b from both sides. Anything subtracted from zero gives its negation.

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

Subtract c from both sides.

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

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

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

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

Solve for b

$$b=-\left(ax^{2}+c\right)$$