What is the general solution for tan^2(θ)+tan(θ)=6,0<= θ<180 ?

The general solution for tan^2(θ)+tan(θ)=6,0<= θ<180 is θ=1.10714…,θ=-1.24904…+180

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tan^2(θ)+tan(θ)=6,0<= θ<180

tan^{2} (θ) + tan (θ) = 6, 0 \leq θ < 18 0^{\circ}

θ = 1.10714 \dots, θ = - 1.24904 \dots + 18 0^{\circ}

Solution steps

tan^{2} (θ) + tan (θ) = 6, 0 \leq θ < 18 0^{\circ}

Solve by substitution

tan (θ) = 2, tan (θ) = - 3

tan (θ) = 2, 0 \leq θ < 18 0^{\circ} : θ = arctan (2)

tan (θ) = - 3, 0 \leq θ < 18 0^{\circ} : θ = - arctan (3) + 18 0^{\circ}

Combine all the solutions

θ = arctan (2), θ = - arctan (3) + 18 0^{\circ}

Show solutions in decimal form

θ = 1.10714 \dots, θ = - 1.24904 \dots + 18 0^{\circ}

sin (2 x) = 5 sin (x)

2 cos^{2} (θ) - 4 cos (θ) - 1 = - 5 cos (θ)

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

tan (x) = - 3 + 2

3 tan (x) - cot (x) = 0

What is the general solution for tan^2(θ)+tan(θ)=6,0<= θ<180 ?
The general solution for tan^2(θ)+tan(θ)=6,0<= θ<180 is θ=1.10714…,θ=-1.24904…+180