What is the general solution for 2tan^2(x)+3tan(x)-2=0 ?

The general solution for 2tan^2(x)+3tan(x)-2=0 is x=0.46364…+pin,x=-1.10714…+pin

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2tan^2(x)+3tan(x)-2=0

2 tan^{2} (x) + 3 tan (x) - 2 = 0

x = 0.46364 \dots + πn, x = - 1.10714 \dots + πn

Solution steps

2 tan^{2} (x) + 3 tan (x) - 2 = 0

Solve by substitution

tan (x) = \frac{1}{2}, tan (x) = - 2

tan (x) = \frac{1}{2} : x = arctan (\frac{1}{2}) + πn

tan (x) = - 2 : x = arctan (- 2) + πn

Combine all the solutions

x = arctan (\frac{1}{2}) + πn, x = arctan (- 2) + πn

Show solutions in decimal form

x = 0.46364 \dots + πn, x = - 1.10714 \dots + πn

sin^{2} (2 x) - \frac{1}{2 3} sin (4 x) = \frac{1}{2}

x, sin (x + x y) = 0

sin (x) = - 3 cos (x)

- 2 sin^{2} (θ) + cos (θ) + 8 = 6

sin^{3} (t) = \frac{1}{8}

What is the general solution for 2tan^2(x)+3tan(x)-2=0 ?
The general solution for 2tan^2(x)+3tan(x)-2=0 is x=0.46364…+pin,x=-1.10714…+pin