#### Answer

The given equation has two unequal rational number solutions.

#### Work Step by Step

Add $26x$ to both sides to obtain:
$$16x^2+3+26x=-26x+26x
\\16x^2+26x+3=0$$
This this equation has $a=16$, $b=26$, and $c=3$.
RECALL:
(1) The discriminant is equal to $b^2-4ac$.
(2) A quadratic equation has the following types of solutions based on the value of the discriminant:
(a) when $b^2-4ac\gt0$, the equation has two unequal rational solutions;
(b) when $b^2-4ac=0$, the equation has one, repeated rational solution; and
(c) when $b^2-4ac\lt0$, the equation has two complex number solutions;
The discriminant of the equation above is:
$$b^2-4ac =26^2 - 4(16)(3) = 676-192=484$$
The discriminant is positive.
Thus, the given equation has two unequal rational number solutions.