The following equations you can use to find the solutions to quadratics (the + changes to a -):
(-b + (b^2 - 4ac)^1/2)/2a
(-b - (b^2 - 4ac)^1/2)/2a
If (b^2 - 4ac) is negative, then it doesn't factorise, as it is to the power of 1/2, which means a sqaure root. You cannot square root a negative number, meaning the quadratic doesn't factorise.