SOLUTION: Please help solve equation: 6 times (s over s + 1) squared plus 5 (s over s + 1) - 6 = 0 Thank you.

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Question 987853: Please help solve equation:
6 times (s over s + 1) squared plus 5 (s over s + 1) - 6 = 0
Thank you.
Answer by ikleyn(52878) About Me  (Show Source):
You can put this solution on YOUR website!
.
Is this the equation you need to solve?

6%2A%28s%2F%28s%2B6%29%29%5E2 + 5%2A%28s%2F%28s%2B1%29%29 - 6 = 0.

If so,  then introduce new variable  x = s%2F%28s%2B1%29.  Then your equation takes the form

6x%5E2 + 5x - 6 = 0.

It is a quadratic equation.  Solve it using the quadratic formula:

x%5B1%2C2%5D = %28-5+%2B-+sqrt%2825+%2B+4%2A6%2A6%29%29%2F12 = %28-5+%2B-+sqrt%2825+%2B+144%29%29%2F12 = %28-5+%2B-+sqrt%28169%29%29%2F12 = %28-5+%2B-+13%29%2F12.

x%5B1%5D = 8%2F12 = 2%2F3.

x%5B2%5D = -18%2F12 = -3%2F2.

Next,  solve two equations

s%2F%28s%2B1%29 = 2%2F3   and   s%2F%28s%2B1%29 = 3%2F2  to get solutions for  s.

Introducing new variable is the standard method for solving non-linear equations like this.