What is the general solution for -5tan^2(θ)+3=8tan(θ)+6 ?

The general solution for -5tan^2(θ)+3=8tan(θ)+6 is θ=(3pi)/4+pin,θ=-0.54041…+pin

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-5tan^2(θ)+3=8tan(θ)+6

- 5 tan^{2} (θ) + 3 = 8 tan (θ) + 6

θ = \frac{3 π}{4} + πn, θ = - 0.54041 \dots + πn

Solution steps

- 5 tan^{2} (θ) + 3 = 8 tan (θ) + 6

Solve by substitution

tan (θ) = - 1, tan (θ) = - \frac{3}{5}

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

tan (θ) = - \frac{3}{5} : θ = arctan (- \frac{3}{5}) + πn

Combine all the solutions

θ = \frac{3 π}{4} + πn, θ = arctan (- \frac{3}{5}) + πn

Show solutions in decimal form

θ = \frac{3 π}{4} + πn, θ = - 0.54041 \dots + πn

cos (θ) = \frac{- 3}{13}

cos (x) = 0.84

cos (2 x) = \frac{( 4 k - 5 )}{10}

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

cos (x + \frac{π}{4}) = 1

What is the general solution for -5tan^2(θ)+3=8tan(θ)+6 ?
The general solution for -5tan^2(θ)+3=8tan(θ)+6 is θ=(3pi)/4+pin,θ=-0.54041…+pin