What is the general solution for 3tan^2(x)+5tan(x)-4=0 ?

The general solution for 3tan^2(x)+5tan(x)-4=0 is x=0.53352…+pin,x=-1.15377…+pin

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3tan^2(x)+5tan(x)-4=0

3 tan^{2} (x) + 5 tan (x) - 4 = 0

x = 0.53352 \dots + πn, x = - 1.15377 \dots + πn

Solution steps

3 tan^{2} (x) + 5 tan (x) - 4 = 0

Solve by substitution

tan (x) = \frac{- 5 + 73}{6}, tan (x) = \frac{- 5 - 73}{6}

tan (x) = \frac{- 5 + 73}{6} : x = arctan (\frac{- 5 + 73}{6}) + πn

tan (x) = \frac{- 5 - 73}{6} : x = arctan (\frac{- 5 - 73}{6}) + πn

Combine all the solutions

x = arctan (\frac{- 5 + 73}{6}) + πn, x = arctan (\frac{- 5 - 73}{6}) + πn

Show solutions in decimal form

x = 0.53352 \dots + πn, x = - 1.15377 \dots + πn

cos (2 x) \cdot 2 = 0

csc^{3} (x) + csc^{2} (x) = 4 csc (x) + 4

2 sin^{2} (x) - 5 sin (x) - 3 = 0

6 + 6 sin (θ) = 4 cos^{2} (θ)

5 cos (x) + 5 sin (x) tan (x) = 10

What is the general solution for 3tan^2(x)+5tan(x)-4=0 ?
The general solution for 3tan^2(x)+5tan(x)-4=0 is x=0.53352…+pin,x=-1.15377…+pin