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

The general solution for 2tan^2(θ)-tan(θ)=3 is θ=0.98279…+pin,θ=(3pi)/4+pin

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2tan^2(θ)-tan(θ)=3

2 tan^{2} (θ) - tan (θ) = 3

θ = 0.98279 \dots + πn, θ = \frac{3 π}{4} + πn

Solution steps

2 tan^{2} (θ) - tan (θ) = 3

Solve by substitution

tan (θ) = \frac{3}{2}, tan (θ) = - 1

tan (θ) = \frac{3}{2} : θ = arctan (\frac{3}{2}) + πn

tan (θ) = - 1 : θ = \frac{3 π}{4} + πn

Combine all the solutions

θ = arctan (\frac{3}{2}) + πn, θ = \frac{3 π}{4} + πn

Show solutions in decimal form

θ = 0.98279 \dots + πn, θ = \frac{3 π}{4} + πn

3 cos (2 θ) - cos (θ) + 1 = 0

170 = \frac{9 0 ^{2}}{16} sin (x) cos (x)

3 cos (x) - 2 sin^{2} (x) = 0

sin (x - \frac{π}{3}) = 0

\frac{- 2 + 3}{2} = - 1 + cos (4 θ + 135)

What is the general solution for 2tan^2(θ)-tan(θ)=3 ?
The general solution for 2tan^2(θ)-tan(θ)=3 is θ=0.98279…+pin,θ=(3pi)/4+pin