What is the general solution for -4tan^2(θ)-4tan(θ)-9=8tan(θ)-4 ?

The general solution for -4tan^2(θ)-4tan(θ)-9=8tan(θ)-4 is θ=-1.19028…+pin,θ=-0.46364…+pin

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-4tan^2(θ)-4tan(θ)-9=8tan(θ)-4

- 4 tan^{2} (θ) - 4 tan (θ) - 9 = 8 tan (θ) - 4

θ = - 1.19028 \dots + πn, θ = - 0.46364 \dots + πn

Solution steps

- 4 tan^{2} (θ) - 4 tan (θ) - 9 = 8 tan (θ) - 4

Solve by substitution

tan (θ) = - \frac{5}{2}, tan (θ) = - \frac{1}{2}

tan (θ) = - \frac{5}{2} : θ = arctan (- \frac{5}{2}) + πn

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

Combine all the solutions

θ = arctan (- \frac{5}{2}) + πn, θ = arctan (- \frac{1}{2}) + πn

Show solutions in decimal form

θ = - 1.19028 \dots + πn, θ = - 0.46364 \dots + πn

cot (4 x) = - \frac{3}{3}

sin (x) = \frac{3.9}{8.1}

5 sin (x) = - 2 cos^{2} (x) + 4

1 + cos (θ) = 1 - cos (θ)

4 cos (x) - 22 = 0

What is the general solution for -4tan^2(θ)-4tan(θ)-9=8tan(θ)-4 ?
The general solution for -4tan^2(θ)-4tan(θ)-9=8tan(θ)-4 is θ=-1.19028…+pin,θ=-0.46364…+pin