3x²-17x+10 = 0

compare to

Ax²+Bx+C = 0

A=3, B=-17, C=10

Substitute in this:




 






Using the +,





  <--that's one solution.

Using the -,





  <--that's the other solution.

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Notice that the problem could have been done by factoring:

 3x²-17x+10 = 0
(x-5)(3x-2) = 0
 x-5=0; 3x-2=0
   x=5;   3x=2
           x=2/3

But they wanted you to do it by the quadratic formula to give
you practice using it.  Not all quadratics are factorable and
we must use the quadratic formula on them.  The ones that won't
factor have irrational square roots, and they wanted to give
you some to do that didn't have those, so the only ones they
could give you were ones that could be done by factoring.

Edwin