Explicação passo-a-passo:

a)

4x²+8x-12=0

∆=8²-4.4.(-12)

∆=64-16.(-12)

∆=64+192

∆=256

x'=-8+√256/2.4=-8+16/8=8/8=1

x"=-8-√256/2.4=-8-16/8=-24/8=-3

b)

x²-x-30=0

∆=(-1)²-4.1.(-30)

∆=1-4.(-30)

∆=1+120

∆=121

x'=-(-1)+√121/2.1=1+11/2=12/2=6

x"=-(-1)-√121/2.1=1-11/2=10/2=5

c)

x²-5x+6=0

∆=(-5)²-4.1.6

∆=25-24

∆=1

x'=-(-5)+√1/2.1=5+1/2=6/2=3

x"=-(-5)-√1/2.1=5-1/2=4/2=2

d)

x²+2x+5=0

∆=2²-4.1.5

∆=4-20

∆=-16

S=∅