First subtract n^2-4n from both sides to get:
4n^2+10n+7 = 0
This is of the form an^2+bn+c = 0, with a=4, b=10 and c=7
The discriminant is given by the formula:
Delta = b^2-4ac = 10^2-(4xx4xx7) = 100-112 = -12
Since Delta < 0 the quadratic has no real solutions. It has two distinct complex roots.
In general, the possible cases are:
Delta = 0 : Means the quadratic has one repeated real root. If the coefficients of the quadratic are rational, that repeated root is also rational.
Delta > 0 : Means that the quadratic has two distinct real roots. If Delta is also a perfect square and the coefficients of the quadratic are rational, then those roots are also rational.
Delta < 0 : Means that the quadratic has no real roots. It has two distinct complex roots which are complex conjugates of one another.
