Question 702644
What are the zeros of the quadratic expression?  Those are critical points for the inequality.  They help you find your solution intervals.

Being brief, {{{x = (6 +- sqrt( 36-4*3*(-5) ))/(6) }}} 
{{{x=1+- (2/3)*sqrt(6)}}}


The x^2 term shows that parabola opens upward and therefore has a minimum.  The minimum will be between the interval x=1-(2/3)(6)^(1/2) and x=1+(2/3)(6)^(1/2).  This minimum being below the horizontal axis, is negative so this interval does NOT satisfy the inequality. 


The solution is therefore, {{{x<1-(2/3)*sqrt(6)}}}  or  {{{x>1+(2/3)*sqrt(6)}}}