The solutions of x(2x-7)=8 may be expressed in the form (m + sqrt(n))/p and (m - sqrt(n))/p, where m, n, and p are relatively prime numbers. Find m+n+p.
+33 x(2x-7)=8
2x^2 - 7x = 8
2x^2 - 7x - 8 = 0
Using the quadratic formula \(\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
\(\frac{7 \pm \sqrt{49+64}}{4}\)
\(\frac{7 \pm \sqrt{113}}{4}\)
\(\frac{7 + \sqrt{113}}{4}\) and \(\frac{7 - \sqrt{113}}{4}\)
So m = 7 n = 113 p = 4
7 + 113 + 4 = \(\boxed{124} \)
