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

The general solution for tan^2(x)-2=3tan(x) is x=1.29706…+pin,x=-0.51166…+pin

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

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

x = 1.29706 \dots + πn, x = - 0.51166 \dots + πn

Solution steps

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

Solve by substitution

tan (x) = \frac{3 + 17}{2}, tan (x) = \frac{3 - 17}{2}

tan (x) = \frac{3 + 17}{2} : x = arctan (\frac{3 + 17}{2}) + πn

tan (x) = \frac{3 - 17}{2} : x = arctan (\frac{3 - 17}{2}) + πn

Combine all the solutions

x = arctan (\frac{3 + 17}{2}) + πn, x = arctan (\frac{3 - 17}{2}) + πn

Show solutions in decimal form

x = 1.29706 \dots + πn, x = - 0.51166 \dots + πn

3 cos (x) + sin (x) = 3

2 tan^{2} (θ) - 2 = 0

sin^{2} (x) = 2 - sin (x)

2 csc (x) cos (x) = csc (x)

2 cot^{2} (2 x) = 6

What is the general solution for tan^2(x)-2=3tan(x) ?
The general solution for tan^2(x)-2=3tan(x) is x=1.29706…+pin,x=-0.51166…+pin