What are the integer solutions of the equation 4x^2-13x+3=0 ?

To decide if the equation has  an integer solution, we'll
have to calculate them, first.

We'll apply quadratic
formula to calculate the solutions of the equation:

x1 =
[-b+sqrt(b^2 - 4ac)]/2a

x2 = [-b-sqrt(b^2 -
4ac)]/2a

a,b,c, are the coefficients of the
quadratic

a = 4, b = -13 , c =
3

x1 = [13+sqrt(169 -
48)]/8

x1 = (13+11)/8

x1 =
24/8

x1 = 3

x2 =
(13-11)/8

x2 = 2/8

x2 =
1/4

Since x2 is not an integer number, we'll
conclude that the only integer solution of the equation is x =
3.