What is the general solution for 4tan^2(x)+14tan(x)+12=0 ?

The general solution for 4tan^2(x)+14tan(x)+12=0 is x=-0.98279…+pin,x=-1.10714…+pin

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4tan^2(x)+14tan(x)+12=0

4 tan^{2} (x) + 14 tan (x) + 12 = 0

x = - 0.98279 \dots + πn, x = - 1.10714 \dots + πn

Solution steps

4 tan^{2} (x) + 14 tan (x) + 12 = 0

Solve by substitution

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

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

tan (x) = - 2 : x = arctan (- 2) + πn

Combine all the solutions

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

Show solutions in decimal form

x = - 0.98279 \dots + πn, x = - 1.10714 \dots + πn

13 (1 - cos (θ)) = sin^{2} (θ)

8 arcsin (x) = 2 π

2 sin (\frac{1}{2} x) + 1 = 0

sin (x) = - \frac{5}{2}

csc (x) = - \frac{7}{6}, tan (x) > 0

What is the general solution for 4tan^2(x)+14tan(x)+12=0 ?
The general solution for 4tan^2(x)+14tan(x)+12=0 is x=-0.98279…+pin,x=-1.10714…+pin