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

The general solution for 2tan^2(θ)+3tan(θ)+4=3 is θ=-0.46364…+pin,θ=(3pi)/4+pin

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2tan^2(θ)+3tan(θ)+4=3

2 tan^{2} (θ) + 3 tan (θ) + 4 = 3

θ = - 0.46364 \dots + πn, θ = \frac{3 π}{4} + πn

Solution steps

2 tan^{2} (θ) + 3 tan (θ) + 4 = 3

Solve by substitution

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

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

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

Combine all the solutions

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

Show solutions in decimal form

θ = - 0.46364 \dots + πn, θ = \frac{3 π}{4} + πn

10 cos (x) = 8

2 sin^{2} (x) = 6 cos^{2} (x)

1 + cot^{2} (θ) = 1.33

x, r + s - 6 t = cos (2 x + y)

cos (x) + cos^{3} (x) = 0

What is the general solution for 2tan^2(θ)+3tan(θ)+4=3 ?
The general solution for 2tan^2(θ)+3tan(θ)+4=3 is θ=-0.46364…+pin,θ=(3pi)/4+pin