+817 The roots of the quadratic equation $x(x-3)=1+8x-5$ may be expressed in the form $\frac{a+\sqrt{b}}{c}$ and $\frac{a-\sqrt{b}}{c}$, where $a$, $b$, and $c$ are prime numbers. Find $abc$.
+129847 x(x-3)=1 + 8x - 5
x^2 - 3x = -4 + 8x
x^2 - 11x = -4 complete the square on x
x^2 - 11x + 121/4 = -4 + 121/4
(x - 11/2)^2 = -16/4 + 121/4
(x - 11/2)^2 = 105/4 we only need one root to find a,b,c
x - (11/2) = sqrt (105) / 2
x = [ 11 + sqrt (105) ] / 2
abc = (11)(105)(2) = 2310
