The solutions of x(3x-7) = 17 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.
+2666 Expand and convert as: \(3x^2-7x-17=0\)
Using the quadratic formula, we have: \( \large {7 \pm \sqrt{7^2-4 \times -17 \times 3} \over 6}\)
This simplifies to: \(\large {{7 \pm \sqrt{253} } \over 6 }\)
Thus, the answer is: \(253 + 7 +6 = \color{brown}\boxed{266}\)
