What is the general solution for tan^2(x)+tan(x)-20=0 ?

The general solution for tan^2(x)+tan(x)-20=0 is x=1.32581…+pin,x=-1.37340…+pin

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tan^2(x)+tan(x)-20=0

tan^{2} (x) + tan (x) - 20 = 0

x = 1.32581 \dots + πn, x = - 1.37340 \dots + πn

Solution steps

tan^{2} (x) + tan (x) - 20 = 0

Solve by substitution

tan (x) = 4, tan (x) = - 5

tan (x) = 4 : x = arctan (4) + πn

tan (x) = - 5 : x = arctan (- 5) + πn

Combine all the solutions

x = arctan (4) + πn, x = arctan (- 5) + πn

Show solutions in decimal form

x = 1.32581 \dots + πn, x = - 1.37340 \dots + πn

8 cos^{2} (x) - 2 = 0

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

2 tan (x) + 2 = 0

0 = sin (2 x)

2 cos^{2} (x) - 3 cos (x) - 2 = 0

What is the general solution for tan^2(x)+tan(x)-20=0 ?
The general solution for tan^2(x)+tan(x)-20=0 is x=1.32581…+pin,x=-1.37340…+pin