The solutions of x(3x-7) = -1+4x may be expressed in the form m + sqrt n / p and m - sqrt n / p , where m, n, and p have a greatest common divisor of 1. Find m+n+p.
x (3x - 7 ) = -1 + 4x
3x^2 - 7x = -1 + 4x simplify as
3x^2 - 11x + 1 = 0
By the Q formula we haxe
solutions = 11 ± sqrt [ 11^2 - ( 4 * 3 * 1 ) ] 11 ± sqrt [ 109 ]
_______________________ = ______________
2 * 3 6
m = 11
n = 109
p = 6
m + n + p = 126
