What is the general solution for 2tan^2(x)-5tan(x)+3=0 ?

The general solution for 2tan^2(x)-5tan(x)+3=0 is x=0.98279…+pin,x= pi/4+pin

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2tan^2(x)-5tan(x)+3=0

2 tan^{2} (x) - 5 tan (x) + 3 = 0

x = 0.98279 \dots + πn, x = \frac{π}{4} + πn

Solution steps

2 tan^{2} (x) - 5 tan (x) + 3 = 0

Solve by substitution

tan (x) = \frac{3}{2}, tan (x) = 1

tan (x) = \frac{3}{2} : x = arctan (\frac{3}{2}) + πn

tan (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

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

Show solutions in decimal form

x = 0.98279 \dots + πn, x = \frac{π}{4} + πn

sin (x) = \frac{2}{9}

sin (x) = \frac{2}{4}

sin (x^{2} - 2 x + 1) = 1

3 - tan^{2} (x) = 0

2 sin^{2} (θ) + cos (θ) = 0

What is the general solution for 2tan^2(x)-5tan(x)+3=0 ?
The general solution for 2tan^2(x)-5tan(x)+3=0 is x=0.98279…+pin,x= pi/4+pin