Find the roots of the quadratic equation by applying the quadratic formula:
$2x^{2} + x + 4 = 0$

(NONE) The given quadratic equation is $2x^{2} + x + 4 = 0$.
On comparing this equation with the standard form $ax^{2} + bx + c = 0$,we obtain:
$a = 2, b = 1, c = 4$.
By using the quadratic formula,$x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$,we substitute the values:
$x = \frac{-1 \pm \sqrt{(1)^{2} - 4(2)(4)}}{2(2)}$
$x = \frac{-1 \pm \sqrt{1 - 32}}{4}$
$x = \frac{-1 \pm \sqrt{-31}}{4}$
Since the discriminant $D = b^{2} - 4ac = -31$,which is less than $0$,the square root of a negative number is not a real number.
Therefore,there are no real roots for the given quadratic equation.