Solve x^2-4by=5

$$x ^ { 2 } - 4 b y = 5$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{x^{2}-5}{4y}\text{, }&y\neq 0\\b\in \mathrm{C}\text{, }&\left(x=\sqrt{5}\text{ or }x=-\sqrt{5}\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

$$-4by=5-x^{2}$$

The equation is in standard form.

$$\left(-4y\right)b=5-x^{2}$$

Divide both sides by -4y.

$$\frac{\left(-4y\right)b}{-4y}=\frac{5-x^{2}}{-4y}$$

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

$$b=\frac{5-x^{2}}{-4y}$$

Divide -x^{2}+5 by -4y.

$$b=-\frac{5-x^{2}}{4y}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{x^{2}-5}{4y}\text{, }&y\neq 0\\b\in \mathrm{R}\text{, }&y=0\text{ and }|x|=\sqrt{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

$$-4by=5-x^{2}$$

The equation is in standard form.

$$\left(-4y\right)b=5-x^{2}$$

Divide both sides by -4y.

$$\frac{\left(-4y\right)b}{-4y}=\frac{5-x^{2}}{-4y}$$

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

$$b=\frac{5-x^{2}}{-4y}$$

Divide 5-x^{2} by -4y.

$$b=-\frac{5-x^{2}}{4y}$$

Solve for x (complex solution)

$$x=-\sqrt{4by+5}$$

$$x=\sqrt{4by+5}$$

Solve for x

$$x=\sqrt{4by+5}$$

$$x=-\sqrt{4by+5}\text{, }\left(y\leq 0\text{ or }b\geq -\frac{5}{4y}\right)\text{ and }\left(y\geq 0\text{ or }b\leq -\frac{5}{4y}\right)$$