SOLUTION: Could you please help me with the following problem? I am supposed to solve this equation using the quadratic formula. (1/y)-(1/y+5)=(1/4) Thank you very much for any help you

Question 88959: Could you please help me with the following problem? I am supposed to solve this equation using the quadratic formula. (1/y)-(1/y+5)=(1/4)
Thank you very much for any help you can provide.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Multiply both sides by the LCD 4y(y+5)

Distribute

Distribute again

Combine like terms

Subtract 20 from both sides

Now let's use the quadratic formula to solve for y:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=5, and c=-20

Square 5 to get 25

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

which split up to

or

Which approximate to

or

So our solutions are:
or

Notice when we graph (just replace y with x), we get:

when we use the root finder feature on a calculator, we find that and .So this verifies our answer
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