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We'll solve the trigonometric equation using substitution technique.
Let cos x = t
t^2 + t - 6 = 0
We'll apply quadratic formula:
t1 = [-1+sqrt(1 + 24)]/2
t1 = (-1 + 5)/2
t1 = 2
t2 = (-1-5)/2
t2 = -3
But cos x = t
cos x = t1 <=> cos x = 2 impossible because the values of cosine function cannot be larger than 1.
cos x = t2 <=> cos x = -3 impossible because the values of cosine function cannot be smaller than -1.
Therefore, the given equation has no solution over the interval (0 , 2`pi` ).
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