To determine the number of real solutions for the quadratic equation \(4x^2 + x + 3 = 0\), we need to calculate the discriminant \(D\) of the quadratic equation, which is given by the formula:
\[ D = b^2 - 4ac \]
where \(a = 4\), \(b = 1\), and \(c = 3\).
Now, we can plug in the values: \[ D = (1)^2 - 4(4)(3) = 1 - 48 = -47 \]
Since the discriminant \(D\) is negative (\(-47 < 0\)), this indicates that the quadratic equation has no real solutions.
Therefore, the answer is: no real solutions.