You have two unknown numbers which multiplied between them results 16 and added equal -17. If you name x as one of such a number and y as the other one, you can write the previous situation in an algebraic way as follow:
x*y = 16 the product is 16
x + y = -17 the addition is -17
to determine which are the numbers you proceed as follow:
y = -17 - x solve for y from the second equation
x(-17-x) = -17 replace previous expression for y into the second equation
x(-17) + x(-x) = -17 use distribution property
-17x - x² = -17
x² + 17x - 17 = 0
Then, you have a quadratic equation, with the following solutions:
x = -17 ± √(17){2