ad2x(ax/b+2c/d)+cb=0,
a2d2x2/b+2acdx+cb=0; multiply through by b/(a2d2):
x2+2abcdx/(a2d2)+bcb/(a2d2)=0,
x2+2bcx/(ad)=-bcb/(a2d2); completing the square:
x2+2bcx/(ad)+(bc/(ad))2=(bc/(ad))2-bcb/(ad)2,
(x+bc/(ad))2=(b2c2-bcb)/(ad)2,
x+bc/(ad)=±√((b2c2-bcb)/(ad),
x=-bc/(ad)±√((b2c2-bcb)/(ad),
x=(-bc±√((b2c2-bcb))/(ad).