Solve 0=b^2-4ac

$$0 = b ^ { 2 } - 4 a c$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{b^{2}}{4c}\text{, }&c\neq 0\\a\in \mathrm{C}\text{, }&b=0\text{ and }c=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$b^{2}-4ac=0$$

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

$$-4ac=-b^{2}$$

The equation is in standard form.

$$\left(-4c\right)a=-b^{2}$$

Divide both sides by -4c.

$$\frac{\left(-4c\right)a}{-4c}=-\frac{b^{2}}{-4c}$$

Dividing by -4c undoes the multiplication by -4c.

$$a=-\frac{b^{2}}{-4c}$$

Divide -b^{2} by -4c.

$$a=\frac{b^{2}}{4c}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{b^{2}}{4c}\text{, }&c\neq 0\\a\in \mathrm{R}\text{, }&b=0\text{ and }c=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$b^{2}-4ac=0$$

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

$$-4ac=-b^{2}$$

The equation is in standard form.

$$\left(-4c\right)a=-b^{2}$$

Divide both sides by -4c.

$$\frac{\left(-4c\right)a}{-4c}=-\frac{b^{2}}{-4c}$$

Dividing by -4c undoes the multiplication by -4c.

$$a=-\frac{b^{2}}{-4c}$$

Divide -b^{2} by -4c.

$$a=\frac{b^{2}}{4c}$$

Solve for b (complex solution)

$$b=-2\sqrt{a}\sqrt{c}$$

$$b=2\sqrt{a}\sqrt{c}$$

Solve for b

$$b=2\sqrt{ac}$$

$$b=-2\sqrt{ac}\text{, }\left(c\geq 0\text{ and }a\geq 0\right)\text{ or }\left(a\leq 0\text{ and }c\leq 0\right)$$