What is the general solution for tan^2(x)+tan(x)-30=0 ?

The general solution for tan^2(x)+tan(x)-30=0 is x=1.37340…+pin,x=-1.40564…+pin

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tan^2(x)+tan(x)-30=0

tan^{2} (x) + tan (x) - 30 = 0

x = 1.37340 \dots + πn, x = - 1.40564 \dots + πn

Solution steps

tan^{2} (x) + tan (x) - 30 = 0

Solve by substitution

tan (x) = 5, tan (x) = - 6

tan (x) = 5 : x = arctan (5) + πn

tan (x) = - 6 : x = arctan (- 6) + πn

Combine all the solutions

x = arctan (5) + πn, x = arctan (- 6) + πn

Show solutions in decimal form

x = 1.37340 \dots + πn, x = - 1.40564 \dots + πn

4 sin (x) cos (x) + 2 sin (x) - 2 cos (x) - 1 = 0

cos (x) - 3 sin (x) = 0

2 cos^{2} (x) + 2 cos (x) - 1 = 0

2 sin^{2} (x) = 0

tan (x) = sin (x)

What is the general solution for tan^2(x)+tan(x)-30=0 ?
The general solution for tan^2(x)+tan(x)-30=0 is x=1.37340…+pin,x=-1.40564…+pin