Solve ar^2+br+c=0

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

Solve for a (complex solution)

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

Steps for Solving Linear Equation

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

$$ar^{2}+c=-br$$

Subtract c from both sides.

$$ar^{2}=-br-c$$

The equation is in standard form.

$$r^{2}a=-br-c$$

Divide both sides by r^{2}.

$$\frac{r^{2}a}{r^{2}}=\frac{-br-c}{r^{2}}$$

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

$$a=\frac{-br-c}{r^{2}}$$

Divide -br-c by r^{2}.

$$a=-\frac{br+c}{r^{2}}$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

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

$$br+c=-ar^{2}$$

Subtract c from both sides.

$$br=-ar^{2}-c$$

The equation is in standard form.

$$rb=-ar^{2}-c$$

Divide both sides by r.

$$\frac{rb}{r}=\frac{-ar^{2}-c}{r}$$

Dividing by r undoes the multiplication by r.

$$b=\frac{-ar^{2}-c}{r}$$

Divide -ar^{2}-c by r.

$$b=-ar-\frac{c}{r}$$

Solve for a

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

Steps for Solving Linear Equation

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

$$ar^{2}+c=-br$$

Subtract c from both sides.

$$ar^{2}=-br-c$$

The equation is in standard form.

$$r^{2}a=-br-c$$

Divide both sides by r^{2}.

$$\frac{r^{2}a}{r^{2}}=\frac{-br-c}{r^{2}}$$

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

$$a=\frac{-br-c}{r^{2}}$$

Divide -br-c by r^{2}.

$$a=-\frac{br+c}{r^{2}}$$

Solve for b

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

Steps for Solving Linear Equation

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

$$br+c=-ar^{2}$$

Subtract c from both sides.

$$br=-ar^{2}-c$$

The equation is in standard form.

$$rb=-ar^{2}-c$$

Divide both sides by r.

$$\frac{rb}{r}=\frac{-ar^{2}-c}{r}$$

Dividing by r undoes the multiplication by r.

$$b=\frac{-ar^{2}-c}{r}$$

Divide -ar^{2}-c by r.

$$b=-ar-\frac{c}{r}$$