To solve this quadratic equation, we can let sin x = u. Then the equation becomes:

u^2 + 3u - 4 = 0

Now we can factor this quadratic equation:

(u + 4)(u - 1) = 0

Setting each factor to zero:

u + 4 = 0 OR u - 1 = 0
u = -4 u = 1

Now substitute back sin x = u:

sin x = -4 OR sin x = 1

Since the sine function's value ranges from -1 to 1, sin x = -4 is not a valid solution. Therefore, the only solution is sin x = 1.

Therefore, x = π/2 + 2nπ, where n is an integer.