# Thread: Intersection of two functions

1. ## Intersection of two functions

Hi

How would one go about finding the intersects of these functions?
$5.5\sqrt{x} + 10000 = C$ and $3.29x = R$

So I made R = C

$5.5\sqrt{x} + 10000 = 3.29x$

Then I'm stuck because I can't see a quadratic there to factorise.

David.

2. Let $X = \sqrt{x}$ to get

$5.5X + 10\,000 = 3.9X^2$

$0 = 3.9X^2 - 5.5X - 10\,000$.

Now solve for $X$, and then you can find $\sqrt{x}$.

3. Bring 10000 to the right of the equation and square both sides.

4. That's awesome.
Thanks for that.
David.

5. I got it out with the first method. It was beautiful.
The second method I tried and I don't know what I did wrong but I couldn't get it out.
I got to here:
$30.25x = 10.8241x^2 - 65800x + 100 000 000$
subtracted 30.25x from both sides and then plugged it into the quadratic formula.
But kept getting two answers, neither of which was the answer to the first method which was also the answer in the back of the book. I must have punched some number into my calculator wrongly.

I will move on now.
Thankyou both for your help
Cheers.
David.