SOLUTION: Which Which two consecutive whole numbers have cubes that differ 2107?

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Question 424991: Which Which two consecutive whole numbers have cubes that differ 2107?
Answer by mananth(16946) About Me  (Show Source):
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(x+1)^3-x^3= 2107
((x+1)-x)((x+1)^2+(x(x+1)+x^2)=2107
1*x^2+2x+1+x^2+x+x^2=2107
3x^2+3x=2106
x^2+x=702
x^2+x-702=0
x^2+27x-26x-702
x(x+27)-26(x+27)=0
(x-26)(x+27)=0
.......
26 & 27
OR
-27 & -26