SOLUTION: 5/2t-t=3+3/2t

Question 88652: 5/2t-t=3+3/2t
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Multiply both sides by 2t

Distribute

Get everything to one side

Combine like terms

Now let's use the quadratic formula to solve for t:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=-2, b=-6, and c=2

Negate -6 to get 6

Square -6 to get 36

Multiply to get

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

Simplify the square root

Multiply 2 and -2 to get -4

So now the expression breaks down into two parts

or

which split up to

or

and simplify to

or

Which approximate to

or

So our solutions are:
or

Notice when we graph (just replace t 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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