A quadratic equation in the standard form ax² + bx + c = 0 where a = 7, b = -18, and c = -11.

Use the unit digit method to quickly narrow down options: $(-18)^2$ ends in 4, and $-4(7)(-11) = 308$ ends in 8. The sum of the unit digits $4 + 8$ ends in 2, identifying C as the only possible candidate.

The most common error is miscalculating the sign of the constant term or forgetting that $(-18)^2$ is positive, often leading students to incorrectly subtract the second part instead of adding.

The discriminant not only determines the value here but also tells us the nature of the roots; since $D > 0$, the quadratic equation has two distinct real roots.