b²-4ac is the discriminant (D)!
you use it when you have a second degree function and want to find the x. If:
D<0 -> no x that we can find
D=0 -> 1 answer for x
D>0 -> 2 answers for x
when your D is = or > 0 then you use these formulas to find the x:
x1= (-b-VD)/2a
x2= (-b+VD)/2a
example1:
f(x)=2x²+3x+4=0
D= b²-4ac
= 3²-4×2×4
=9- 32
=-23
-> no answers for x
example2:
f(x)=2x²+5x+2=0
D= 4²-4×2×2
= 25-16
=9
x1= (-b-VD)/2a
= (-5-3)/4
= -8/4
=-2
x2= (-b+VD)/2a
= (-5+3)/4
=-2/4
=-1/2