What is the general solution for 8tan^2(θ)+15tan(θ)-15=2tan(θ)-9 ?

The general solution for 8tan^2(θ)+15tan(θ)-15=2tan(θ)-9 is θ=0.35877…+pin,θ=-1.10714…+pin

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8tan^2(θ)+15tan(θ)-15=2tan(θ)-9

8 tan^{2} (θ) + 15 tan (θ) - 15 = 2 tan (θ) - 9

θ = 0.35877 \dots + πn, θ = - 1.10714 \dots + πn

Solution steps

8 tan^{2} (θ) + 15 tan (θ) - 15 = 2 tan (θ) - 9

Solve by substitution

tan (θ) = \frac{3}{8}, tan (θ) = - 2

tan (θ) = \frac{3}{8} : θ = arctan (\frac{3}{8}) + πn

tan (θ) = - 2 : θ = arctan (- 2) + πn

Combine all the solutions

θ = arctan (\frac{3}{8}) + πn, θ = arctan (- 2) + πn

Show solutions in decimal form

θ = 0.35877 \dots + πn, θ = - 1.10714 \dots + πn

6 tan (x) = 23

tan (- 3 x) = 1

sin^{2} (x) = cos^{2} (\frac{x}{2})

x, sin (x) = 2

(2 sin (x) - 1) = 0

What is the general solution for 8tan^2(θ)+15tan(θ)-15=2tan(θ)-9 ?
The general solution for 8tan^2(θ)+15tan(θ)-15=2tan(θ)-9 is θ=0.35877…+pin,θ=-1.10714…+pin