The product of half my number times my number is 162

This can be solved by a simple linear equation and a substitution. Let's assume that n is my number. So as per the equation:

n x n/2 = 162

Which means, n^2 = 162 x 2

Which means, n^2 = 324

Which means, n = √324

Which means, n = - + 18

Both 18 and - 18 could be my number, since it is not mentioned my number is positive or negative.