What is the general solution for tan^2(θ)+tan(θ)-6=0 ?

The general solution for tan^2(θ)+tan(θ)-6=0 is θ=1.10714…+pin,θ=-1.24904…+pin

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tan^2(θ)+tan(θ)-6=0

tan^{2} (θ) + tan (θ) - 6 = 0

θ = 1.10714 \dots + πn, θ = - 1.24904 \dots + πn

Solution steps

tan^{2} (θ) + tan (θ) - 6 = 0

Solve by substitution

tan (θ) = 2, tan (θ) = - 3

tan (θ) = 2 : θ = arctan (2) + πn

tan (θ) = - 3 : θ = arctan (- 3) + πn

Combine all the solutions

θ = arctan (2) + πn, θ = arctan (- 3) + πn

Show solutions in decimal form

θ = 1.10714 \dots + πn, θ = - 1.24904 \dots + πn

tan (θ) = 2 sin (θ), 0 \leq θ \leq 2 π

2 sin (x) tan (x) - tan (x) = 0

sin (x) = sin (3 x)

7 tan (θ) + 5 = 0

sin (x + 4 5^{\circ}) = \frac{3}{2}

What is the general solution for tan^2(θ)+tan(θ)-6=0 ?
The general solution for tan^2(θ)+tan(θ)-6=0 is θ=1.10714…+pin,θ=-1.24904…+pin