Question 1011574
x^3-8=-14 +7x
x^3-7x+6=0
with synthetic division, using 
1/1;;0;;-7;;6
the roots are (x-1)(x2+x-6)
the second factors
(x-1)(x+3)(x-2)
Three possible roots, 1,2, and -3.  These are roots of the changed equation, not the original one, where 2 cannot be a solution.
The sum of the solutions is 1-3=-2
{{{graph(300,200,-10,10,-10,10,x^3-7x+6)}}}