See if you can factor $5x^2 - 11x - 12$ into a product of two binomials of the form $(ax + b)(cx + d)$.

You need two numbers that multiply to $5 \cdot (-12)$ and add to $-11$. Think about factor pairs of $-60$ that sum to $-11$.

Once you have factored the quadratic, set each factor equal to zero to find both solutions, then decide which one matches what the question is asking for.

In Desmos, type y = 5x^2 - 11x - 12 to graph the quadratic function.

Look for the points where the graph crosses the x-axis. Click on each x-intercept; Desmos will display their coordinates. The x-coordinates of these intercepts are the solutions to the equation.

Among the x-intercepts you see, identify which x-value is positive. That is the positive solution to the equation.

The equation $5x^2 - 11x - 12 = 0$ is a quadratic equation in standard form $ax^2 + bx + c = 0$, where $a=5$, $b=-11$, and $c=-12$. Quadratic equations can often be solved efficiently by factoring.

We want to factor $5x^2 - 11x - 12$ into the form $(mx + n)(px + q)$.

Look for two numbers that multiply to $5 \cdot (-12) = -60$ and add to $-11$. Those numbers are $-15$ and $4$.

Rewrite the middle term using $-15x$ and $4x$:

Now factor by grouping:

Factor out $(x - 3)$:

We now have

For a product to be zero, at least one factor must be zero:

• $5x + 4 = 0$
• $x - 3 = 0$

Solve each linear equation to obtain two real roots—one negative and one positive. We will identify the requested solution in the next step.

The two solutions are $x = -\frac{4}{5}$ and $x = 3$. The question specifically asks for the positive solution, so we choose $x = 3$.

Final answer: $3$.