Question 910231
{{{x^2+5x+c=what}}}, you should equate this to something if you are looking for solutions or "no solutions".


Maybe you wanted, {{{x^2+5x+c=0}}} and are asking for what value c will this have no solutions?  Why would this equation have no solutions?


{{{x=(-5+- sqrt(5^2-4*c))/2}}}
{{{highlight(x=(-5+- sqrt(25-4c))/2)}}}.
The equation will have either ONE or TWO solutions.  


If you want the equation to have NO REAL SOLUTIONS, then the necessary condition is {{{25-4c<0}}}, in which case, x will contain an imaginary number.  You can solve this inequality for c.