#7R^2-14R+10# is of the form #aR^2+bR+c# with #a=7#, #b=-14# and #c=10#.
This has discriminant #Delta# given by the formula:
#Delta = b^2-4ac = (-14)^2-(4xx7xx10) = 196 - 280 = -84#
Since #Delta < 0# the equation #7R^2-14R+10 = 0# has no real roots. It has a pair of complex roots that are complex conjugates of one another.
The possible cases are:
#Delta > 0# The quadratic equation has two distinct real roots. If #Delta# is a perfect square (and the coefficients of the quadratic are rational), then those roots are also rational.
#Delta = 0# The quadratic equation has one repeated real root.
#Delta < 0# The quadratic equation has no real roots. It has a pair of distinct complex roots that are complex conjugates of one another.
