What is the general solution for 2tan^2(x)+5tan(x)+3=0 ?

The general solution for 2tan^2(x)+5tan(x)+3=0 is x=(3pi)/4+pin,x=-0.98279…+pin

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2tan^2(x)+5tan(x)+3=0

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

x = \frac{3 π}{4} + πn, x = - 0.98279 \dots + πn

Solution steps

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

Solve by substitution

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

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

tan (x) = - \frac{3}{2} : x = arctan (- \frac{3}{2}) + πn

Combine all the solutions

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

Show solutions in decimal form

x = \frac{3 π}{4} + πn, x = - 0.98279 \dots + πn

csc^{2} (x) = 4

3 tanh (2 θ) = 5 sech (θ) + 1

2 cos^{2} (θ) + cos (θ) = 1

tan (x) sin (x) - sin (x) = 0

2 sin (x) = csc (x)

What is the general solution for 2tan^2(x)+5tan(x)+3=0 ?
The general solution for 2tan^2(x)+5tan(x)+3=0 is x=(3pi)/4+pin,x=-0.98279…+pin