Solve x=frac{-b+sqrt{4ac}}{2a}

$$x = \frac { - b + \sqrt { 4 a c } } { 2 a }$$

Solve for b (complex solution)

$$b=2\left(-ax+\sqrt{ac}\right)$$

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2a.

$$x\times 2a=-b+\sqrt{4ac}$$

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

$$-b+\sqrt{4ac}=x\times 2a$$

Subtract \sqrt{4ac} from both sides.

$$-b=x\times 2a-\sqrt{4ac}$$

The equation is in standard form.

$$-b=2ax-\sqrt{4ac}$$

Divide both sides by -1.

$$\frac{-b}{-1}=\frac{2ax-2\sqrt{ac}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$b=\frac{2ax-2\sqrt{ac}}{-1}$$

Divide 2xa-2\sqrt{ac} by -1.

$$b=-2ax+2\sqrt{ac}$$

Solve for b

$$b=2\left(-ax+\sqrt{ac}\right)$$

$$\left(c\geq 0\text{ and }a>0\right)\text{ or }\left(c\leq 0\text{ and }a<0\right)$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2a.

$$x\times 2a=-b+\sqrt{4ac}$$

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

$$-b+\sqrt{4ac}=x\times 2a$$

Subtract \sqrt{4ac} from both sides.

$$-b=x\times 2a-\sqrt{4ac}$$

The equation is in standard form.

$$-b=2ax-\sqrt{4ac}$$

Divide both sides by -1.

$$\frac{-b}{-1}=\frac{2ax-2\sqrt{ac}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$b=\frac{2ax-2\sqrt{ac}}{-1}$$

Divide 2xa-2\sqrt{ac} by -1.

$$b=-2ax+2\sqrt{ac}$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{bx-\sqrt{c\left(c-2bx\right)}-c}{2x^{2}}\text{, }&\left(b\neq 0\text{ and }x\neq 0\text{ and }c=0\right)\text{ or }\left(arg(c)<\pi \text{ and }c\neq 0\text{ and }x\neq 0\text{ and }arg(ax+\frac{b}{2})<\pi \right)\text{ or }\left(b\neq 0\text{ and }x\neq 0\text{ and }arg(ax+\frac{b}{2})<\pi \right)\\a=-\frac{bx+\sqrt{c\left(c-2bx\right)}-c}{2x^{2}}\text{, }&\left(b\neq 0\text{ and }x\neq 0\text{ and }c=0\right)\text{ or }\left(arg(c)\geq \pi \text{ and }c\neq 0\text{ and }x\neq 0\text{ and }arg(ax+\frac{b}{2})<\pi \right)\text{ or }\left(b\neq 0\text{ and }x\neq 0\text{ and }arg(ax+\frac{b}{2})<\pi \right)\\a=\frac{b^{2}}{4c}\text{, }&b\neq 0\text{ and }c\neq 0\text{ and }x=0\text{ and }arg(b)<\pi \\a\neq 0\text{, }&c=0\text{ and }b=0\text{ and }x=0\end{matrix}\right.$$