What is the general solution for 3tan^2(x)+7tan(x)+4=0 ?

The general solution for 3tan^2(x)+7tan(x)+4=0 is x=(3pi)/4+pin,x=-0.92729…+pin

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3tan^2(x)+7tan(x)+4=0

3 tan^{2} (x) + 7 tan (x) + 4 = 0

x = \frac{3 π}{4} + πn, x = - 0.92729 \dots + πn

Solution steps

3 tan^{2} (x) + 7 tan (x) + 4 = 0

Solve by substitution

tan (x) = - 1, tan (x) = - \frac{4}{3}

tan (x) = - 1 : x = \frac{3 π}{4} + πn

tan (x) = - \frac{4}{3} : x = arctan (- \frac{4}{3}) + πn

Combine all the solutions

x = \frac{3 π}{4} + πn, x = arctan (- \frac{4}{3}) + πn

Show solutions in decimal form

x = \frac{3 π}{4} + πn, x = - 0.92729 \dots + πn

cos (2 θ) - 3 = - 5 sin (θ)

sin (2 x) = 0

7 sin^{2} (x) + 3 cos^{2} (x) = 5

sin (x) = 0.3746

0 = 2 + 4 cos (θ)

What is the general solution for 3tan^2(x)+7tan(x)+4=0 ?
The general solution for 3tan^2(x)+7tan(x)+4=0 is x=(3pi)/4+pin,x=-0.92729…+pin