Solve dy=-0.25x^2+4x-17

$$d y = - 0.25 x ^ { 2 } + 4 x - 17$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=-\frac{x^{2}-16x+68}{4y}\text{, }&y\neq 0\\d\in \mathrm{C}\text{, }&\left(x=8-2i\text{ or }x=8+2i\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$yd=-\frac{x^{2}}{4}+4x-17$$

Divide both sides by y.

$$\frac{yd}{y}=\frac{-\frac{x^{2}}{4}+4x-17}{y}$$

Dividing by y undoes the multiplication by y.

$$d=\frac{-\frac{x^{2}}{4}+4x-17}{y}$$

Divide -\frac{x^{2}}{4}+4x-17 by y.

$$d=\frac{-x^{2}+16x-68}{4y}$$

Solve for d

$$d=-\frac{x^{2}-16x+68}{4y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$yd=-\frac{x^{2}}{4}+4x-17$$

Divide both sides by y.

$$\frac{yd}{y}=\frac{-\frac{x^{2}}{4}+4x-17}{y}$$

Dividing by y undoes the multiplication by y.

$$d=\frac{-\frac{x^{2}}{4}+4x-17}{y}$$

Divide -\frac{x^{2}}{4}+4x-17 by y.

$$d=\frac{-x^{2}+16x-68}{4y}$$

Solve for x (complex solution)

$$x=-2\sqrt{-dy-1}+8$$

$$x=2\left(\sqrt{-dy-1}+4\right)$$

Solve for x

$$x=-2\sqrt{-dy-1}+8$$

$$x=2\sqrt{-dy-1}+8\text{, }\left(y>0\text{ or }d\geq -\frac{1}{y}\right)\text{ and }\left(y<0\text{ or }d\leq -\frac{1}{y}\right)\text{ and }y\neq 0$$