Question 760578
{{{x^2 > 5x-8}}}

{{{x^2-5x+8 > 5x-8-5x+8}}}
{{{x^2-5x+8>0}}}


The quadratic expression is not factorable.  You cannot use 8 and 1 whichever sign combination you use; and you cannot use 2 and 4, whichever sign combination you use.  Just use general solution to quadratic formula to find the critical points (where the quadratic expression would be zero).


Critical points for  inequality at:
{{{(5+- sqrt(25-4*8))/(2)}}} which are complex with imaginary parts.
Same as {{{(5+- sqrt(-7))/2}}}


The given inequality does NOT intersect the x-axis so has no real critical points.  Just check any point for x.  Either the inequality is true or it is false, for ALL values of x.