Question 524345
A) Examine the "discriminant" This is the quantity under the radical sign in the quadratic formula: {{{b^2-4ac}}}.
a) If the discriminant is zero {{{b^2-4ac = 0}}} there is "one" solution! 
N.B. There are really two roots but they are identical.
B) If the discriminant is positive {{{b^2-4ac > 0}}} there are two real roots.
C) If the discriminant is negative {{{b^2-4ac < 0}}} there are "no" real solutions. 
N.B. The solutions in this case are complex roots.
B) Here's an example:
{{{4x^2+6x-3 = 0}}} Here: a = 4, b = 6, and c = -3, so
{{{b^2-4ac = 36-4(4)(-3)}}} = {{{84}}}
The discriminant is positive so there are two real roots.