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

The general solution for 5tan^2(x)-3tan(x)-2=0 is x= pi/4+pin,x=-0.38050…+pin

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

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

x = \frac{π}{4} + πn, x = - 0.38050 \dots + πn

Solution steps

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

Solve by substitution

tan (x) = 1, tan (x) = - \frac{2}{5}

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = - \frac{2}{5} : x = arctan (- \frac{2}{5}) + πn

Combine all the solutions

x = \frac{π}{4} + πn, x = arctan (- \frac{2}{5}) + πn

Show solutions in decimal form

x = \frac{π}{4} + πn, x = - 0.38050 \dots + πn

- 2 sin (θ) (1 + cos (θ)) = 0

2 sec^{2} (2 x) = 3 tan (2 x) + 1

4 cot (x) + 5 = 9

2 = \frac{1}{2} [1 + arctan (\frac{1}{1 + C})]

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

What is the general solution for 5tan^2(x)-3tan(x)-2=0 ?
The general solution for 5tan^2(x)-3tan(x)-2=0 is x= pi/4+pin,x=-0.38050…+pin