SAT Question 7a6d06bf: Nonlinear Functions answer and explanation with Desmos solution

Let $x$ represent the width, in inches, of the rectangle. It's given that the length of the rectangle is $4$ inches less than $7$ times its width, or $7x-4$ inches. The area of a rectangle is equal to its width multiplied by its length. Multiplying the width, $x$ inches, by the length, $7x-4$ inches, yields $x\left(7x-4\right)$ square inches. It's given that the rectangle has an area of $155$ square inches, so it follows that $x\left(7x-4\right)=155$, or $7x^2-4x=155$. Subtracting $155$ from both sides of this equation yields $7x^2-4x-155=0$. Factoring the left-hand side of this equation yields $\left(7x+31\right)\left(x-5\right)=0$. Applying the zero product property to this equation yields two solutions: $x=-\frac{31}{7}$ and $x=5$. Since $x$ is the rectangle's width, in inches, which must be positive, the value of $x$ is $5$. Therefore, the width of the rectangle, in inches, is $5$.