The sum of a number and 24 times its reciprocal is 11. find the numbers

x + 24(1/x) = 11 
Solve for x:   x = 8 or x = 3

Solve for x over the real numbers:
x + 24/x = 11

Bring x + 24/x together using the common denominator x:
(x^2 + 24)/x = 11

Multiply both sides by x:
x^2 + 24 = 11 x

Subtract 11 x from both sides:
x^2 - 11 x + 24 = 0

The left hand side factors into a product with two terms:
(x - 8) (x - 3) = 0

Split into two equations:
x - 8 = 0 or x - 3 = 0

Add 8 to both sides:
x = 8 or x - 3 = 0

Add 3 to both sides:
  x = 8 or x = 3