Let x be the middle number, so the three consecutive odd numbers are 

    (x-2),  x  and  (x+2),   in ascending order.


Then you write the equation as you read the problem

    x*(x+2) = 3*(x-2) + 26.


You simplify this quadratic equation

    x^2 + 2x = 3x - 6 + 26


and write it in the standard form'

    x^2 - x - 20 = 0.


Then you factor its left side

    (x-5)*(x+4) = 0,


and you see that it has the roots  x= 5  and x= -4.


-4 is not an odd number, so the only meaningful solution is  x= 5.


Thus the three numbers are  3,  5,  7.


It is the ANSWER, and you can CHECK it on your own, that the answer satisfies the problem's conditions.