How do you solve 2sin^2x-2sinx-1=0? The answer has to be between [0, 2pi)?

So it's 2sin²(x) - 2sin(x) -1= 0

Solution
sin=x
We now have 2x²-2x-1=0
x1=[-b+[2^2-4*2*(-1)]^1/2]/2*2=(4+12^1/2)/4=(2+3^1/2)/2
but x1>1 so we have an
UNDEFINED SOLUTION BECAUSE -1<=sin<=1<x1

x2=[-b-[2^2-4*2*(-1)]^1/2]/2*2=(4-12^1/2)/4=(2-3^1/2)/2
ACCEPTABLE SOLUTION because 0<x2<1

Now we have sin=(2-3^1/2)/2
Transform x2=(2-3^1/2)/2 into a known sinx
Let's say sinA=x2=(2-3^1/2)/2

So we have sin=x2=sinA(=(2-3^1/2)/2)
Solutions
x=2*k*(pi)+ A (#1)
x=2*k*(pi)- A (#2)

k is a number that belongs in Z (whole numbers)
A is our wanted angle.
Take equation (#1) and put it between [0,2pi)

0<=2*k*pi+A<2pi, add (-a)
-A<=2*k*pi<2pi-A, multiply with 1/2*pi for which is (1/2*pi)>0

So we have -A/2*pi<=k<1-A/2*pi.

Now A should be an angle with pi in it, eg A=pi/2 or A=54pi/67 something like those.
Siplify all pis and you'll have something like

number b<=k<number c (no pis)
Choose a WHOLE number between [number b,number c)
That number is your k.

Replace k in (#1) That's your first solution.

Do almost the same with (#2)
Write #2 between [0,2pi)
Add (+a), multiply with 1/2pi, simplify pis and etc.
Choose you k (it should be a different number or coincidentally the same, but it's a whole number)
Replace your second k in #2

So those two x from #1 and #2 are your wanted xs and thus the solution of this equation for [0,2pi)

My comments on this exercise.

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Sorry if it is confusing, but because I'm greek I don't know the correct mathematical terms in english and for now I won't bother to add them.

Also, det=(b^2-4*a*c) turns out to be an unsuitable for this exercise number. That's why I said sina=x2
If x1, or x2 was a nice number, a sinx that I know of, like x2=1/2, so A in that case would be 60rad=pi/3, (because sinA=sinpi/3=1/2), it would be better for everyone.
I really hope you messed up the equation otherwise if that wasn't a typo then all I have to say is that I can't help you with finding your right sinA.
However.
The logic of this exercise is always the same. Like the one above. So once you find your A you're okay to follow this.
Excuse any mistakes, though I'm pretty sure everything is correct.