What is the general solution for 4tan^2(x)+7tan(x)-4=0 ?

The general solution for 4tan^2(x)+7tan(x)-4=0 is x=0.42598…+pin,x=-1.14481…+pin

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4tan^2(x)+7tan(x)-4=0

4 tan^{2} (x) + 7 tan (x) - 4 = 0

x = 0.42598 \dots + πn, x = - 1.14481 \dots + πn

Solution steps

4 tan^{2} (x) + 7 tan (x) - 4 = 0

Solve by substitution

tan (x) = \frac{- 7 + 113}{8}, tan (x) = \frac{- 7 - 113}{8}

tan (x) = \frac{- 7 + 113}{8} : x = arctan (\frac{- 7 + 113}{8}) + πn

tan (x) = \frac{- 7 - 113}{8} : x = arctan (\frac{- 7 - 113}{8}) + πn

Combine all the solutions

x = arctan (\frac{- 7 + 113}{8}) + πn, x = arctan (\frac{- 7 - 113}{8}) + πn

Show solutions in decimal form

x = 0.42598 \dots + πn, x = - 1.14481 \dots + πn

tan (θ) = - 1 - 3

y, v = (1 - 4 cos (5 y))^{- \frac{1}{2}}

x, cos (x) = cos (p)

cot (a) - 1 = 0

csc (θ) = - \frac{3}{5}

What is the general solution for 4tan^2(x)+7tan(x)-4=0 ?
The general solution for 4tan^2(x)+7tan(x)-4=0 is x=0.42598…+pin,x=-1.14481…+pin