What is the general solution for 2tan^2(x)+9tan(x)+7=0 ?

The general solution for 2tan^2(x)+9tan(x)+7=0 is x=(3pi)/4+pin,x=-1.29249…+pin

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2tan^2(x)+9tan(x)+7=0

2 tan^{2} (x) + 9 tan (x) + 7 = 0

x = \frac{3 π}{4} + πn, x = - 1.29249 \dots + πn

Solution steps

2 tan^{2} (x) + 9 tan (x) + 7 = 0

Solve by substitution

tan (x) = - 1, tan (x) = - \frac{7}{2}

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

tan (x) = - \frac{7}{2} : x = arctan (- \frac{7}{2}) + πn

Combine all the solutions

x = \frac{3 π}{4} + πn, x = arctan (- \frac{7}{2}) + πn

Show solutions in decimal form

x = \frac{3 π}{4} + πn, x = - 1.29249 \dots + πn

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

cos (5 t) - cos (3 t) = sin (4 t)

2 sin^{2} (θ) - 1 = 0, 0 \leq θ < 2 π

2 cosh (2 x) = 5 sinh (x) + 3

tan (x) = \frac{6.9}{6.6}

What is the general solution for 2tan^2(x)+9tan(x)+7=0 ?
The general solution for 2tan^2(x)+9tan(x)+7=0 is x=(3pi)/4+pin,x=-1.29249…+pin