What is the general solution for 4tan^2(θ)+16tan(θ)=7tan(θ)-2 ?

The general solution for 4tan^2(θ)+16tan(θ)=7tan(θ)-2 is θ=-0.24497…+pin,θ=-1.10714…+pin

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4tan^2(θ)+16tan(θ)=7tan(θ)-2

4 tan^{2} (θ) + 16 tan (θ) = 7 tan (θ) - 2

θ = - 0.24497 \dots + πn, θ = - 1.10714 \dots + πn

Solution steps

4 tan^{2} (θ) + 16 tan (θ) = 7 tan (θ) - 2

Solve by substitution

tan (θ) = - \frac{1}{4}, tan (θ) = - 2

tan (θ) = - \frac{1}{4} : θ = arctan (- \frac{1}{4}) + πn

tan (θ) = - 2 : θ = arctan (- 2) + πn

Combine all the solutions

θ = arctan (- \frac{1}{4}) + πn, θ = arctan (- 2) + πn

Show solutions in decimal form

θ = - 0.24497 \dots + πn, θ = - 1.10714 \dots + πn

10 (1 - cos (θ)) = sin^{2} (θ)

cos (2 x) = 2 - 5 cos (x)

tan (x - 20) = cot (x + 45)

sin (z) = 4

- 63 = - 9 csc (3 x)

What is the general solution for 4tan^2(θ)+16tan(θ)=7tan(θ)-2 ?
The general solution for 4tan^2(θ)+16tan(θ)=7tan(θ)-2 is θ=-0.24497…+pin,θ=-1.10714…+pin