What is the general solution for 4tan^2(θ)-2tan(θ)+3=-7tan(θ)+2 ?

The general solution for 4tan^2(θ)-2tan(θ)+3=-7tan(θ)+2 is θ=-0.24497…+pin,θ=(3pi)/4+pin

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4tan^2(θ)-2tan(θ)+3=-7tan(θ)+2

4 tan^{2} (θ) - 2 tan (θ) + 3 = - 7 tan (θ) + 2

θ = - 0.24497 \dots + πn, θ = \frac{3 π}{4} + πn

Solution steps

4 tan^{2} (θ) - 2 tan (θ) + 3 = - 7 tan (θ) + 2

Solve by substitution

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

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

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

Combine all the solutions

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

Show solutions in decimal form

θ = - 0.24497 \dots + πn, θ = \frac{3 π}{4} + πn

- 2 = csc (θ)

2 cot (x) = csc^{2} (x)

2 csc (2 x) cot (2 x) = 0

3 cos (y) + cot (y) = 0

2 sin (x) - 3 sin (x) + 1 = 0

What is the general solution for 4tan^2(θ)-2tan(θ)+3=-7tan(θ)+2 ?
The general solution for 4tan^2(θ)-2tan(θ)+3=-7tan(θ)+2 is θ=-0.24497…+pin,θ=(3pi)/4+pin