Solve yx^2+bx+c=0,x

$$y x ^ { 2 } + b x + c = 0 , x$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

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

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

Subtract c from both sides.

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

The equation is in standard form.

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

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

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

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

Solve for b

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

Steps for Solving Linear Equation

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

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

Subtract c from both sides.

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

The equation is in standard form.

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

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

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

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

Solve for c

$$c=-x\left(xy+b\right)$$