What is the general solution for 3tan^2(θ)+7tan(θ)-2=-4 ?

The general solution for 3tan^2(θ)+7tan(θ)-2=-4 is θ=-0.32175…+pin,θ=-1.10714…+pin

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3tan^2(θ)+7tan(θ)-2=-4

3 tan^{2} (θ) + 7 tan (θ) - 2 = - 4

θ = - 0.32175 \dots + πn, θ = - 1.10714 \dots + πn

Solution steps

3 tan^{2} (θ) + 7 tan (θ) - 2 = - 4

Solve by substitution

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

tan (θ) = - \frac{1}{3} : θ = arctan (- \frac{1}{3}) + πn

tan (θ) = - 2 : θ = arctan (- 2) + πn

Combine all the solutions

θ = arctan (- \frac{1}{3}) + πn, θ = arctan (- 2) + πn

Show solutions in decimal form

θ = - 0.32175 \dots + πn, θ = - 1.10714 \dots + πn

8 sin (2 x) + 1 = 6

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

6 sin (a) + 4 = 2 sin (a) + 8

sin (3 x) = 0, - 2 < x < 2

tan (x) = \frac{2}{6}

What is the general solution for 3tan^2(θ)+7tan(θ)-2=-4 ?
The general solution for 3tan^2(θ)+7tan(θ)-2=-4 is θ=-0.32175…+pin,θ=-1.10714…+pin