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

The general solution for tan^2(x)+3tan(x)-5=0 is x=0.87300…+pin,x=-1.33665…+pin

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

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

x = 0.87300 \dots + πn, x = - 1.33665 \dots + πn

Solution steps

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

Solve by substitution

tan (x) = \frac{- 3 + 29}{2}, tan (x) = \frac{- 3 - 29}{2}

tan (x) = \frac{- 3 + 29}{2} : x = arctan (\frac{- 3 + 29}{2}) + πn

tan (x) = \frac{- 3 - 29}{2} : x = arctan (\frac{- 3 - 29}{2}) + πn

Combine all the solutions

x = arctan (\frac{- 3 + 29}{2}) + πn, x = arctan (\frac{- 3 - 29}{2}) + πn

Show solutions in decimal form

x = 0.87300 \dots + πn, x = - 1.33665 \dots + πn

tan (\frac{1}{2} x) - 3 = 0

2 cos (2 θ) = 6 cos (θ) - 4

5 sin (θ) - 4 = 2 sin (θ) - 6

cos (2 θ) - cos (4 θ) = 0

tan (x) = 1.4

What is the general solution for tan^2(x)+3tan(x)-5=0 ?
The general solution for tan^2(x)+3tan(x)-5=0 is x=0.87300…+pin,x=-1.33665…+pin