Question

23 times a positive integer is more than twice it's square by 63. Find the integer.

Answer 1

Let the positive integer =  x

23x  - 2*x^2  = 63

2x^2 - 23x  + 63 = 0

2x^2 - 14x - 9x  + 63 = 0

2x(x - 7) - 9(x - 7) = 0

(x - 7)(2x - 9) = 0

x-7 = 0,  2x - 9 = 0

x = 7,  x = 4.5

Answer is  x = 7