Solve the inequation: 4x^2+ 8x + 3 > 0

We'll use another method to determine the interval of x
values where the given expression is positive.

According to
the rule, between the roots of the expression 4x^2+ 8x + 3, the expression has the
opposite sign of the coefficient of x^2 and outside the roots, the expression has the
same sign as the coefficient of x^2.

We'll calculate the
roots:

4x^2+ 8x + 3 = 0

We'll
apply the quadratic formula:

x1 = [-8 +
sqrt(64-48)]/8

x1 = (-8 +
4)/8

x1 =
-1/2

x2 =
(-8-4)/8

x2 =
-3/2

So, the expression is
positive over the
intervals:

(-inf.,
-3/2)U(-1/2,+inf.)