What is the general solution for 4tan^2(x)+5tan(x)-6=0 ?

The general solution for 4tan^2(x)+5tan(x)-6=0 is x=0.64350…+pin,x=-1.10714…+pin

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4tan^2(x)+5tan(x)-6=0

4 tan^{2} (x) + 5 tan (x) - 6 = 0

x = 0.64350 \dots + πn, x = - 1.10714 \dots + πn

Solution steps

4 tan^{2} (x) + 5 tan (x) - 6 = 0

Solve by substitution

tan (x) = \frac{3}{4}, tan (x) = - 2

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

tan (x) = - 2 : x = arctan (- 2) + πn

Combine all the solutions

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

Show solutions in decimal form

x = 0.64350 \dots + πn, x = - 1.10714 \dots + πn

sin (x) = \frac{1}{2}, 0 \leq x < 2 π

cos (t) + cos (2 t) = - 1

sin (θ) = \frac{3}{4}

3 cos (t) = 0

cos (θ) = \frac{7}{9}

What is the general solution for 4tan^2(x)+5tan(x)-6=0 ?
The general solution for 4tan^2(x)+5tan(x)-6=0 is x=0.64350…+pin,x=-1.10714…+pin