Question 278943
graphically
if the parabola touches the x axis twice there are two solutions
if it touches once there is one solution
if it never touches the x axis there are no real solutions

algebraically
x^+4x+4=0
x^2-2x-3=0
x^2-2x+3=0
check out the determinants in these three equations
*[invoke quadratic "x", 1, 4, 4 ]
*[invoke quadratic "x", 1, -2, -3 ]
*[invoke quadratic "x", 1, -2, 3 ]