anyone good at maths please pop up

Solve 2tan^2 theta = 15tan theta - 7 in the interval - 180 deg < theta < 360 deg Give your solution(s) correct to 2 decimal places where appropriate.
I have been able to figure out 4 solutions for the question above but the question requires 6.
Please help!!

Post what you've done - we will help

So i let tantheta = x (like a quadratic)
then I made the equation equal to 0 :
2x^2 - 15x + 7
then i factorised normally (2x-1) (x-7)
then i got two solutions to be : 1/2 and 7 then substituting tan back in:
tanx = 1/2
i got x= 26.57
then using the cast diagram i got another solution to be : x= 206.57 (2dp)
then for tanx = 7
i got x= 81.87(2dp)
then using the cast diagram, my other solution was :
261.87
so as you can see my four solutions were:
26.57,206.57,81.87 and 261.87
but the question requires six solutions?!

What about the rest of the range? Aren't there more solutions between -180 and 0

thats what Im stuck on , i dont know how to find the negative solutions

Go in the other direction on your cast diagram, past zero, and into the negatives.

whyy?

Thats how you get the negative solutions. Since tan (and sin and cos) are periodic, there are an infinite number of solutions that occur at regular intervals. Imagine a tan graph that goes on forever to negative and positive infinity, there will be infinitely many solutions in each direction. By going backwards on your cast diagram you can find the negative solutions. Put them in your calculator and see that it gives the same answer as the positive solutions.

do i subtract 360 or 180 to find the negative values

What does the graph look like? That will give you your answer ...
Remember you can always check by substitution.

i didnt use a graph it was a cast diagram

i have not seen this before and im currently doing gcse fm 😭

Really? The graphs are part of GCSE!

well i think we will learn this later on in the year , but ill read more on it , but the question i have is if they also want values for negative theta, how do i use the CAST diagram to find the solutions that are also negative?

You go round the CAST diagram clockwise [-ve turn] from 0 and will see that tan is +ve between -90 and -180 [see link with graph]
Can you find the angles now?

do i go round the cast diagram clockwise from the principal value?