Solve the quadratic inequality 3x^2-13x-10>0.

To solve the inequality above, first we have to calculate
the roots of the equation 3x^2-13x-10 = 0.

After finding
the roots of the equation, we could write the expression in a factored form
as:

3(x-x1)(x-x2)>0

So,
let's apply the quadratic formula to calculate the
roots:

x1 =
[13+sqrt(169-120)]/6

x1 =
(13+sqrt49)/6

x1 =
(13+7)/6

x1 =
10/3

x2 =
(13-7)/6

x2 =
6/6

x2 =
1

The inequality will be written
as:

3(x -
10/3)(x-1)>0

We'll divide by
3:

(x -
10/3)(x-1)>0

Now, we'll discuss the
inequality:

- the product is positive if the factors are
both positive:

x -
10/3>0

x>10/3

and

x-1>0

x>1

So,
x belongs to the interval (10/3 , +inf.)

- the product is
positive if the factors are both negative:

x -
10/3<0

x<10/3

x-1<0

x<1

So,
x belongs to the interval ( -inf.,1)

Finally, the solution
set of the inequality is the union of the sets identified
above:

( -inf.,1) U (10/3 ,
+inf.)