What is the general solution for 3tan^2(x)+10tan(x)+7=0 ?

The general solution for 3tan^2(x)+10tan(x)+7=0 is x=(3pi)/4+pin,x=-1.16590…+pin

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3tan^2(x)+10tan(x)+7=0

3 tan^{2} (x) + 10 tan (x) + 7 = 0

x = \frac{3 π}{4} + πn, x = - 1.16590 \dots + πn

Solution steps

3 tan^{2} (x) + 10 tan (x) + 7 = 0

Solve by substitution

tan (x) = - 1, tan (x) = - \frac{7}{3}

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

tan (x) = - \frac{7}{3} : x = arctan (- \frac{7}{3}) + πn

Combine all the solutions

x = \frac{3 π}{4} + πn, x = arctan (- \frac{7}{3}) + πn

Show solutions in decimal form

x = \frac{3 π}{4} + πn, x = - 1.16590 \dots + πn

8 sin (x) - 8 = 0

3 cos (x) + 1 = sec (x)

3 sin (θ) + 1 = sin (θ)

40 cos (\frac{2 π}{3} t) - 71 = - 80

- 2 cos (x) - 2 cos (2 x) = 0

What is the general solution for 3tan^2(x)+10tan(x)+7=0 ?
The general solution for 3tan^2(x)+10tan(x)+7=0 is x=(3pi)/4+pin,x=-1.16590…+pin