SOLUTION: If one of the two roots of the equation (10x + 7)( 3x - 2) + ax + 9 = 0 is -5/6, what is the other root?

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Question 1089868: If one of the two roots of the equation (10x + 7)( 3x - 2) + ax + 9 = 0 is -5/6, what is the other root?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%2810x+%2B+7%29%28+3x+-+2%29+%2B+ax+%2B+9+=+0 one root is -5%2F6
%2810%28-5%2F6%29+%2B+7%29%28+3%28-5%2F6%29+-+2%29+%2B+a%28-5%2F6%29+%2B+9+=+0
6+-5a%2F6+%2B+9+=+0

15+-5a%2F6++=+0
5a%2F6=15+
a=90%2F5+

%2810x+%2B+7%29%28+3x+-+2%29+%2B+%2890%2F5%29x+%2B+9+=+0
30+x%5E2+%2B+x+-+14+%2B+%2890%2F5%29x+%2B+9+=+0
30+x%5E2+%2B+19+x+-+5+=+0
%285+x+-+1%29+%286+x+%2B+5%29+=+0
roots:

if %285+x+-+1%29++=+0->x=1%2F5
if +%286+x+%2B+5%29+=+0->x=-5%2F6 (given)
so, the other root is x=1%2F5