Super urgent!

Solve the equation for all real values of x. 3tan^2 = sqrt3 tanx

f (x) = tan2 (x) + (√3 - 1) [tan (x) ] - √3 = 0

tan2 (x) + √3[tan (x) ] - tan (x) - √3 = 0

Factor into

[-1 + tan (x) ]*[√3 + tan (x) ] = 0

which means

[-1 + tan (x) ] = 0 and/or [√3 + tan (x) ] = 0

Then

tan (x) = 1

tan-1 (1) = pi/4 radians

For the other equation

[√3 + tan (x) ] = 0

tan (x) = - √3

tan-1 (-√3) = - pi/3

so that

x = pi/4 or - pi/3 in the interval [0, 2pi]