What is the general solution for 3tan^2(x)+5tan(x)+2=0 ?

The general solution for 3tan^2(x)+5tan(x)+2=0 is x=-0.58800…+pin,x=(3pi)/4+pin

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3tan^2(x)+5tan(x)+2=0

3 tan^{2} (x) + 5 tan (x) + 2 = 0

x = - 0.58800 \dots + πn, x = \frac{3 π}{4} + πn

Solution steps

3 tan^{2} (x) + 5 tan (x) + 2 = 0

Solve by substitution

tan (x) = - \frac{2}{3}, tan (x) = - 1

tan (x) = - \frac{2}{3} : x = arctan (- \frac{2}{3}) + πn

tan (x) = - 1 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = arctan (- \frac{2}{3}) + πn, x = \frac{3 π}{4} + πn

Show solutions in decimal form

x = - 0.58800 \dots + πn, x = \frac{3 π}{4} + πn

sin (2 x + \frac{π}{3}) = - \frac{3}{2}

tan (2 θ) + 2 cos (θ) = 0, 0 \leq θ \leq 2 π

cos (2 x) + 10 sin^{2} (x) = 5

2 = 3 + 2 sin (θ)

- 2 sin (θ) + sin (2 θ) = 0

What is the general solution for 3tan^2(x)+5tan(x)+2=0 ?
The general solution for 3tan^2(x)+5tan(x)+2=0 is x=-0.58800…+pin,x=(3pi)/4+pin