Question 1039815
{{{x^2+4x+8<0}}}


If put as a graph for {{{y=x^2+4x+8}}}, and you check were {{{y<0}}},
{{{graph(400,400,-10,5,-5,10,x^2+4x+8)}}}
you understand that for real numbers, no solution.


You can solve the original inequality for Complex numbers, and use Completing the Square in the process.  Look for your lessons on that.  You would find within the solution, an expression,  {{{4^2-4*1*8}}}, your inequality's discriminant.  


D for discriminant,
{{{D=16-32}}}
{{{D=-16}}}


Roots are {{{x=(-4+- sqrt(-16))/2}}}
{{{x=(-4+- 4i)/2}}}
{{{x=-2+- 2i}}}
...and your solution is for x BETWEEN these roots.  The trouble with that is, complex numbers do not have order.  NO SOLUTION.