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3 sin x ± 4√1 - sin² x = 5
± 4√1 - sin² x = 5 - 3 sin x
(4√1 - sin²x)² = (5 - 3 sinx)²
16(1 - sin²x) = 25 - 30 sin x + 9 sin²x
16 - 16sin²x = 25 - 30 sinx + 9sin²x
-16 sin²x - 9 sin²x + 30 sinx + 16 - 25 = 0
-25 sin²x + 30 sinx - 9 = 0
25 sin²x - 30 sinx + 9 = 0
sin x = -b ± √b² - 4ac / 2a
a = 25
b = -30
c = 9
sin x = 30 ± √(-30)² - 4(25)(9) / 2.25
= 30 ± √900 - 900 / 50
= 30 ± 0 / 50
= 30 / 50
= 3 / 5