Identify the conic section $$$\frac{x \left(250 - x\right)}{20} = \frac{125}{4}$$$

Identify and find the properties of the conic section $$$\frac{x \left(250 - x\right)}{20} = \frac{125}{4}$$$.

The general equation of a conic section is $$$A x^{2} + B x y + C y^{2} + D x + E y + F = 0$$$.

In our case, $$$A = \frac{1}{20}$$$, $$$B = 0$$$, $$$C = 0$$$, $$$D = - \frac{25}{2}$$$, $$$E = 0$$$, $$$F = \frac{125}{4}$$$.

The discriminant of the conic section is $$$\Delta = 4 A C F - A E^{2} - B^{2} F + B D E - C D^{2} = 0$$$.

Next, $$$B^{2} - 4 A C = 0$$$.

Since $$$\Delta = 0$$$, this is the degenerated conic section.

Since $$$B^{2} - 4 A C = 0$$$, the equation represents two parallel lines.

$$$\frac{x \left(250 - x\right)}{20} = \frac{125}{4}$$$A represents a pair of the lines $$$x = 125 - 50 \sqrt{6}$$$, $$$x = 50 \sqrt{6} + 125$$$A.

General form: $$$\frac{x^{2}}{20} - \frac{25 x}{2} + \frac{125}{4} = 0$$$A.

Factored form: $$$\left(x - 125 - 50 \sqrt{6}\right) \left(x - 125 + 50 \sqrt{6}\right) = 0$$$A.

Graph: see the graphing calculator.