let 'x' be the certain positive number, x > 0

the product of one less then a certain positive number and two less then three time the number is 14

(x - 1) (3x - 2) = 14

by simplifying and solving the quadratic equation we find and consider only the positive roots thus

x = 3

click here to see the step by step solution of the equation

Click to see all the steps

indeed

(3 - 1)(3*3 - 2) = 2*7 = 14

the number is 3.