What is the general solution for 2tan^2(x)+11tan(x)+9=0 ?

The general solution for 2tan^2(x)+11tan(x)+9=0 is x=(3pi)/4+pin,x=-1.35212…+pin

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2tan^2(x)+11tan(x)+9=0

2 tan^{2} (x) + 11 tan (x) + 9 = 0

x = \frac{3 π}{4} + πn, x = - 1.35212 \dots + πn

Solution steps

2 tan^{2} (x) + 11 tan (x) + 9 = 0

Solve by substitution

tan (x) = - 1, tan (x) = - \frac{9}{2}

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

tan (x) = - \frac{9}{2} : x = arctan (- \frac{9}{2}) + πn

Combine all the solutions

x = \frac{3 π}{4} + πn, x = arctan (- \frac{9}{2}) + πn

Show solutions in decimal form

x = \frac{3 π}{4} + πn, x = - 1.35212 \dots + πn

cos (x) = 0.37

2 cos (2 θ) - 3 = 0

3 arccos (4 x) = 2 π

cos (3 x) = cos (x)

tan (x + 3 2^{\circ}) = cot (x - 2 0^{\circ})

What is the general solution for 2tan^2(x)+11tan(x)+9=0 ?
The general solution for 2tan^2(x)+11tan(x)+9=0 is x=(3pi)/4+pin,x=-1.35212…+pin