Tan^2x +5tanx +3=0
approximate to four decimal places the solutions for x,
0 less than or equal to x< 2pi

The given equation is

Where , this interval means that we need to find the solution of the equation in every quadrant, remember that trigonometric equations are periodical, that means its solution repeats in other quadrants.

First, we need to make a variable change where and , so the equation is

Now, we can solve the equation as a quadratic equation.

We know this equation has two solutions

To find these solutions, we use the quadratic formula

Where

Replacing these values, we have

So,

But, , so

360 different combinations