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.
