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

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

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

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

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

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

Solve by substitution

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

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = - 3 :

No Solution

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x, cos (x) = 1

cos (x) cot^{2} (x) = cos (x)

4 sin (x) cos (x) = - 9 cos (x)

cos (t) = - \frac{3}{2}

- 7 sin (7 x) = 0

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