What is the general solution for -8tan^2(θ)-4tan(θ)-11=6tan(θ)-8 ?

The general solution for -8tan^2(θ)-4tan(θ)-11=6tan(θ)-8 is θ=-0.64350…+pin,θ=-0.46364…+pin

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-8tan^2(θ)-4tan(θ)-11=6tan(θ)-8

- 8 tan^{2} (θ) - 4 tan (θ) - 11 = 6 tan (θ) - 8

θ = - 0.64350 \dots + πn, θ = - 0.46364 \dots + πn

Solution steps

- 8 tan^{2} (θ) - 4 tan (θ) - 11 = 6 tan (θ) - 8

Solve by substitution

tan (θ) = - \frac{3}{4}, tan (θ) = - \frac{1}{2}

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

tan (θ) = - \frac{1}{2} : θ = arctan (- \frac{1}{2}) + πn

Combine all the solutions

θ = arctan (- \frac{3}{4}) + πn, θ = arctan (- \frac{1}{2}) + πn

Show solutions in decimal form

θ = - 0.64350 \dots + πn, θ = - 0.46364 \dots + πn

2 cos^{2} (x) + 3 cos (x) - 5 = 0

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

4 cos (2 x) = 2

cos (x) = \frac{5}{4}

sin^{2} (2 x) = \frac{1}{2}

What is the general solution for -8tan^2(θ)-4tan(θ)-11=6tan(θ)-8 ?
The general solution for -8tan^2(θ)-4tan(θ)-11=6tan(θ)-8 is θ=-0.64350…+pin,θ=-0.46364…+pin