SAT Question 17d0e87d: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice C is correct. Dividing each side of the given equation by $2$ yields $\frac{14x}{14y}=\frac{2\sqrt{w+19}}{2}$, or $\frac{x}{y}=\sqrt{w+19}$. Because it's given that each of the variables is positive, squaring each side of this equation yields the equivalent equation ${\left(\frac{x}{y}\right)}^2=w+19$. Subtracting $19$ from each side of this equation yields ${\left(\frac{x}{y}\right)}^2-19=w$, or $w={\left(\frac{x}{y}\right)}^2-19$.