What is the general solution for 2sin^2(x)+5sin(x)-12=0 ?

The general solution for 2sin^2(x)+5sin(x)-12=0 is No Solution for x\in\mathbb{R}

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2sin^2(x)+5sin(x)-12=0

2 sin^{2} (x) + 5 sin (x) - 12 = 0

No Solution for x \in R

Solution steps

2 sin^{2} (x) + 5 sin (x) - 12 = 0

Solve by substitution

sin (x) = \frac{3}{2}, sin (x) = - 4

sin (x) = \frac{3}{2} :

No Solution

sin (x) = - 4 :

No Solution

Combine all the solutions

No Solution for x \in R

3 tan (x - \frac{π}{5}) - 1 = 0

x, 0 = 4 - \frac{1}{cos ^{2} ( x )}

tan (θ) = \frac{17}{12}

csc^{2} (θ) = 2 cot (θ)

tan (2 x) = + \frac{8}{15}

What is the general solution for 2sin^2(x)+5sin(x)-12=0 ?
The general solution for 2sin^2(x)+5sin(x)-12=0 is No Solution for x\in\mathbb{R}