After you set the right sides equal, rearrange the equation so everything is on one side and the other side is zero. What kind of equation do you get, and what method can you use if it doesn’t factor nicely?

When you solve the quadratic, you will get two values for $x$. Check which one is positive, because the question only wants the positive solution.

In Desmos, type y = 3x - 2 to graph the straight line.

On a new line in Desmos, type y = x^2 - 5 to graph the parabola.

Tap or click on each point where the line and the parabola intersect. Desmos will show the coordinates of these intersection points, including their $x$-values.

Look at the positive $x$-coordinate of the intersection point. Then, in Desmos, type each answer choice expression (for example, (3 + sqrt(21))/2) on separate lines to see their decimal values, and choose the option whose value matches the positive intersection $x$-coordinate.

Because both equations equal $y$, set their right-hand sides equal to each other:

This equation will give the $x$-values where the graphs intersect (the solutions to the system).

Move all terms to one side to get a standard quadratic equation:

So you need to solve $x^2 - 3x - 3 = 0$. It does not factor nicely, so use the quadratic formula.

For the quadratic $ax^2 + bx + c = 0$, the solutions are given by

Here, $a = 1$, $b = -3$, and $c = -3$. Substitute these values:

This expression will simplify to two real solutions for $x$.},{

Now simplify the expression from the quadratic formula:

There are two solutions: $x = \frac{3 + \sqrt{21}}{2}$ and $x = \frac{3 - \sqrt{21}}{2}$. The second one is negative (since $\sqrt{21} > 3$), and the problem asks for the positive solution. Therefore, the correct answer is $\boxed{\dfrac{3 + \sqrt{21}}{2}}$, which corresponds to choice B.