The quadratic function f(x)=2x^2-24x+c has two zeros that differ by 18. find the value of c.

For this case we have the following function:
  f (x) = 2x ^ 2-24x + c
  We set zero to find the roots of the function.
  We have then:
  2x ^ 2-24x + c = 0
  x ^ 2-12x + c / 2 = 0
  Factoring we have:
  (x - / + x1) (x - / + x2) = 0
  On the other hand we have:
  x2-x1 = 18
  x2 + x1 = -12
  Solving the system we have:
  x1 = -15
  x2 = 3
  Substituting we have:
  (x-15) (x + 3) = 0
  Rewriting:
  x ^ 2 -12x - 45 = 0
  Therefore, the value of c is given by:
  c / 2 = -45
  c = -90
  
  the value of c is:
  c = -90