What is the general solution for 2tan^2(x)+9tan(x)+3=0 ?

The general solution for 2tan^2(x)+9tan(x)+3=0 is x=-0.34780…+pin,x=-1.33364…+pin

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2tan^2(x)+9tan(x)+3=0

2 tan^{2} (x) + 9 tan (x) + 3 = 0

x = - 0.34780 \dots + πn, x = - 1.33364 \dots + πn

Solution steps

2 tan^{2} (x) + 9 tan (x) + 3 = 0

Solve by substitution

tan (x) = \frac{- 9 + 57}{4}, tan (x) = \frac{- 9 - 57}{4}

tan (x) = \frac{- 9 + 57}{4} : x = arctan (\frac{- 9 + 57}{4}) + πn

tan (x) = \frac{- 9 - 57}{4} : x = arctan (\frac{- 9 - 57}{4}) + πn

Combine all the solutions

x = arctan (\frac{- 9 + 57}{4}) + πn, x = arctan (\frac{- 9 - 57}{4}) + πn

Show solutions in decimal form

x = - 0.34780 \dots + πn, x = - 1.33364 \dots + πn

sin^{2} (x) = (\frac{2 m - 4}{5})

1.25 cos^{2} (θ) + 0.694 cos (θ) - 0.519 = 0

sec (θ) = \frac{13}{12}

6 sin (x) - 3 = 0

sin (7 0^{\circ}) = 1.15 sin (x)

What is the general solution for 2tan^2(x)+9tan(x)+3=0 ?
The general solution for 2tan^2(x)+9tan(x)+3=0 is x=-0.34780…+pin,x=-1.33364…+pin