What is the general solution for 5tan^2(θ)-tan(θ)+12=8tan(θ)+8 ?

The general solution for 5tan^2(θ)-tan(θ)+12=8tan(θ)+8 is θ= pi/4+pin,θ=0.67474…+pin

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5tan^2(θ)-tan(θ)+12=8tan(θ)+8

5 tan^{2} (θ) - tan (θ) + 12 = 8 tan (θ) + 8

θ = \frac{π}{4} + πn, θ = 0.67474 \dots + πn

Solution steps

5 tan^{2} (θ) - tan (θ) + 12 = 8 tan (θ) + 8

Solve by substitution

tan (θ) = 1, tan (θ) = \frac{4}{5}

tan (θ) = 1 : θ = \frac{π}{4} + πn

tan (θ) = \frac{4}{5} : θ = arctan (\frac{4}{5}) + πn

Combine all the solutions

θ = \frac{π}{4} + πn, θ = arctan (\frac{4}{5}) + πn

Show solutions in decimal form

θ = \frac{π}{4} + πn, θ = 0.67474 \dots + πn

16 sin^{2} (θ) - 4 = 0

22 cos (x) - 2 = 0

cos^{2} (x) + 2 sin (x) = 0

cos (3 θ) = \frac{1}{2}

sin (3 x + 5) = cos (4 x + 1)

What is the general solution for 5tan^2(θ)-tan(θ)+12=8tan(θ)+8 ?
The general solution for 5tan^2(θ)-tan(θ)+12=8tan(θ)+8 is θ= pi/4+pin,θ=0.67474…+pin