Trig.

2sin^2x-3sinx=-1

sin^2x-3sinx=-1/2 times -3

sq. root of (sin^2x)+sinx= sq. root of 3/sq. root of 2

sinx+sinx=(sq. root of 3 times sq. root of 2)/2

2sinx=(sq. root of 3 times sq. root of 2)/2)) times 1/2

(sq. root of 3 times sq. root of 2)/sq. root of 4))=sinx

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1. 2sin^2(x)-3sinx=-1
2sin^2(x)-3sinx+1=0
(2sinx-1)(sinx-1)=0
2sinx=1 or sinx=1
sinx=1/2 or sinx =1
x=30, 150 or x=90

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