You have to know this fact:
If the quadratic equation:

x² + bx + c = 0

has roots r1 and r2, then b = -(r1 + r2) and c = r1r2

So if the quadratic equation:

x² + bx + c = 0

is to has roots r1 =  and r2 = ,
then b = -(r1 + r2) =  =

 =

 =  =  = 

and c = r1r2 =   = 
 =  =
 =  =  = 

So the equation

x² + bx + c = 0

becomes

x² + 1x +  = 0

But that doesn't have integer coefficients, so we clear of
fractions so it will:

So we multiply every term by LCD = 4

4x² + 4x +  = 0

4x² + 4x - 31 = 0 

Now that one has only integer coefficients.

Edwin