What is the general solution for 4tan^2(x)+12tan(x)-27=0 ?

The general solution for 4tan^2(x)+12tan(x)-27=0 is x=0.98279…+pin,x=-1.35212…+pin

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4tan^2(x)+12tan(x)-27=0

4 tan^{2} (x) + 12 tan (x) - 27 = 0

x = 0.98279 \dots + πn, x = - 1.35212 \dots + πn

Solution steps

4 tan^{2} (x) + 12 tan (x) - 27 = 0

Solve by substitution

tan (x) = \frac{3}{2}, tan (x) = - \frac{9}{2}

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

tan (x) = - \frac{9}{2} : x = arctan (- \frac{9}{2}) + πn

Combine all the solutions

x = arctan (\frac{3}{2}) + πn, x = arctan (- \frac{9}{2}) + πn

Show solutions in decimal form

x = 0.98279 \dots + πn, x = - 1.35212 \dots + πn

sin^{2} (x) - cos (x) = \frac{1}{4}

cos^{4} (a) = 3 + 4 cos^{2} (a) + cos^{4} (a)

cos^{4} (t) = 1

8 cos^{2} (x) - 12 sin (x) - 12 = 0

1 - cos (x) = 2

What is the general solution for 4tan^2(x)+12tan(x)-27=0 ?
The general solution for 4tan^2(x)+12tan(x)-27=0 is x=0.98279…+pin,x=-1.35212…+pin