SOLUTION: Solve the equation. 3/y=y/5y-12

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Question 156967: Solve the equation.
3/y=y/5y-12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%2Fy=y%2F%285y-12%29 Start with the given equation



3%285y-12%29=y%28y%29 Cross multiply


15y-36=y%28y%29 Distribute


15y-36=y%5E2 Multiply


15y-36-y%5E2=0 Subtract y%5E2 from both sides


-y%5E2%2B15y-36=0 Rearrange the terms.


Notice we have a quadratic equation in the form of ay%5E2%2Bby%2Bc where a=-1, b=15, and c=-36


Let's use the quadratic formula to solve for y


y+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


y+=+%28-%2815%29+%2B-+sqrt%28+%2815%29%5E2-4%28-1%29%28-36%29+%29%29%2F%282%28-1%29%29 Plug in a=-1, b=15, and c=-36


y+=+%28-15+%2B-+sqrt%28+225-4%28-1%29%28-36%29+%29%29%2F%282%28-1%29%29 Square 15 to get 225.


y+=+%28-15+%2B-+sqrt%28+225-144+%29%29%2F%282%28-1%29%29 Multiply 4%28-1%29%28-36%29 to get 144


y+=+%28-15+%2B-+sqrt%28+81+%29%29%2F%282%28-1%29%29 Subtract 144 from 225 to get 81


y+=+%28-15+%2B-+sqrt%28+81+%29%29%2F%28-2%29 Multiply 2 and -1 to get -2.


y+=+%28-15+%2B-+9%29%2F%28-2%29 Take the square root of 81 to get 9.


y+=+%28-15+%2B+9%29%2F%28-2%29 or y+=+%28-15+-+9%29%2F%28-2%29 Break up the expression.


y+=+%28-6%29%2F%28-2%29 or y+=++%28-24%29%2F%28-2%29 Combine like terms.


y+=+3 or y+=+12 Simplify.


So the answers are y+=+3 or y+=+12