Solve the inequality: 17x + 5 >= -6x^2.

17x + 5 >= -6x^2

First
we will move -6x^2 to the left side so the right side is
0.

==> 6x^2 + 17x + 5 >=
0

Now we have a quadratic function, we will use the
quadratic formula to find the roots.

==> x1= ( -17 +
sqrt(289-4*6*5) / 2*6

             = (-17 + 13) / 12 =
-4/12 = -1/3

==> ( x+1/3 ) Or ( 3x+1) is a factor of
the function.

==> x2= ( -17-13) /12 = -30/12 =
-5/2

==> (x+5/2) OR (2x + 5) is a
factor.

==> ( 2x+5) ( 3x+1)
>=0

Then ( 2x+5) >= 0   and ( 3x+1)
>=0

==> x >= -5/2  and   x>=
-1/3

==> x = [ -1/3,
inf)

OR:

 x =<-5/2  
and  x=< =-1/3

==> x = (-inf,
-5/2]

==> x = (-inf, -5/2] U [-1/3,
inf)