Solve 96p^2+(y-x)p-y=0*xp

$$96 p ^ { 2 } + ( y - x ) p - y = 0 \cdot x p$$

Solve for x

$$\left\{\begin{matrix}x=y+96p-\frac{y}{p}\text{, }&p\neq 0\\x\in \mathrm{R}\text{, }&p=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply y-x by p.

$$96p^{2}+yp-xp-y=0xp$$

Anything times zero gives zero.

$$96p^{2}+yp-xp-y=0$$

Subtract 96p^{2} from both sides. Anything subtracted from zero gives its negation.

$$yp-xp-y=-96p^{2}$$

Subtract yp from both sides.

$$-xp-y=-96p^{2}-yp$$

Add y to both sides.

$$-xp=-96p^{2}-yp+y$$

The equation is in standard form.

$$\left(-p\right)x=-py+y-96p^{2}$$

Divide both sides by -p.

$$\frac{\left(-p\right)x}{-p}=\frac{-py+y-96p^{2}}{-p}$$

Dividing by -p undoes the multiplication by -p.

$$x=\frac{-py+y-96p^{2}}{-p}$$

Divide -96p^{2}-yp+y by -p.

$$x=y+96p-\frac{y}{p}$$

Solve for p

$$p=\frac{\sqrt{x^{2}-2xy+y^{2}+384y}+x-y}{192}$$

$$p=\frac{-\sqrt{x^{2}-2xy+y^{2}+384y}+x-y}{192}\text{, }y\geq x+\frac{\sqrt{147456-1536x}}{2}-192\text{ or }y\leq x-\frac{\sqrt{147456-1536x}}{2}-192\text{ or }x\geq 96$$