A quadratic equation in the form 3x² - 7x + 2 = 0.

Mentally calculate $b^2$ ($49$) and $4ac$ ($4 imes 3 imes 2 = 24$), then subtract them directly: $49 - 24 = 25$.

Students often forget the negative sign on the coefficient $b = -7$, however, since $(-7)^2$ is positive, the sign error usually does not affect this specific result, but it is critical in finding roots.

The discriminant determines the nature of the roots; if $D > 0$, the roots are real and distinct, which is a common check for nature of roots questions in coordinate geometry.