1. ## Solve the equation

How would I go about solving this?

$\displaystyle 6x^2+17x-39=0$

EDIT: Factorised into $\displaystyle (-13+-3x)(3+-2x)=0$But that didn't help

2. Originally Posted by Mukilab
How would I go about solving this?

$\displaystyle 6x^2+17x-39=0$

EDIT: Factorised into $\displaystyle (-13+-3x)(3+-2x)=0$But that didn't help
You have that (-13 - 3x)(3 - 2x) = 0 . Therefore either (3 - 2x) = 0 , or (-13 - 3x) = 0.

Can you solve from here?

3. (3 - 2x) = 0 , or (-13 - 3x) = 0.

therefore

$\displaystyle x=1.5$ or $\displaystyle x=\frac{-13}{3}$

It has to be one definite answer though. It tells me from this I should be able to calculate a side in a polygon (I need to find x). Do I try subbing both into the formula and see which works?

4. Originally Posted by Mukilab
(3 - 2x) = 0 , or (-13 - 3x) = 0.

therefore

$\displaystyle x=1.5$ or $\displaystyle x=\frac{-13}{3}$

It has to be one definite answer though. It tells me from this I should be able to calculate a side in a polygon (I need to find x). Do I try subbing both into the formula and see which works?
If you're measuring a side on a polygon is follows that $\displaystyle x>0$ as you're measuring a length. So discard the negative root

5. Originally Posted by Mukilab
(3 - 2x) = 0 , or (-13 - 3x) = 0.

therefore

$\displaystyle x=1.5$ or $\displaystyle x=\frac{-13}{3}$

It has to be one definite answer though. It tells me from this I should be able to calculate a side in a polygon (I need to find x). Do I try subbing both into the formula and see which works?
Both are correct answers to the equation, but only one is the answer you seek for the given problem. Only one of the answers makes sense as the length of a polygon's side, can you see which one and why?

6. Originally Posted by Mukilab

Do I try subbing both into the formula and see which works?
Not really, you can do it as a check, both should give 0.

7. Originally Posted by e^(i*pi)
If you're measuring a side on a polygon is follows that $\displaystyle x>0$ as you're measuring a length. So discard the negative root
Ok

Originally Posted by pomp
Both are correct answers to the equation, but only one is the answer you seek for the given problem. Only one of the answers makes sense as the length of a polygon's side, can you see which one and why?
Originally Posted by pickslides
Not really, you can do it as a check, both should give 0.
Thank you for all the posts, most considerate.