SOLUTION: Please help me understand this. Thanks! 1/(4x + 2) - x/3 = -21/(10x + 5)

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: Please help me understand this. Thanks! 1/(4x + 2) - x/3 = -21/(10x + 5)      Log On


   

Question 544158: Please help me understand this. Thanks!
1/(4x + 2) - x/3 = -21/(10x + 5)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%284x+%2B+2%29 - x%2F3 = %28-21%29%2F%2810x+%2B+5%29
Factoring the denominators will help
1%2F%282%282x+%2B+1%29%29 - x%2F3 = %28-21%29%2F%285%282x+%2B+1%29%29
:
get rid of the some of the denominators, multiply by 30, results:
15%2F%28%282x+%2B+1%29%29 - 10x = 6%28-21%29%2F%28%282x+%2B+1%29%29
15%2F%28%282x+%2B+1%29%29 - 10x = %28-126%29%2F%28%282x+%2B+1%29%29
:
Multiply by (2x+1) and you have
15 - 10x(2x+1) = -126
-20x^2 - 10x = -126 - 15
-20x^2 - 10x = -141
:
Get rid of all those negatives, mult by -1
20x^2 + 10x = +141
20x^2 + 10x - 141 = 0
Solve this quadratic equation using the quadratic formula
I got: x = 2.417 and x = -2.917
these look like unlikely solutions, however, I check them both out in the original problem and got equality.