1. **State the problem:** Find the gradient of the line $L$ given by the equation $$2y + 7x = 10.$$\n\n2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y = mx + c,$$ where $m$ is the gradient.\n\nStarting with $$2y + 7x = 10,$$ subtract $7x$ from both sides:\n$$2y = -7x + 10.$$\n\n3. **Divide both sides by 2 to solve for $y$:**\n$$y = \frac{-7x + 10}{2} = -\frac{7}{2}x + 5.$$\n\n4. **Identify the gradient:** The coefficient of $x$ in the slope-intercept form is the gradient.\n$$\boxed{\text{Gradient} = -\frac{7}{2}}.$$