S(x)=2x+7,43
D(x)=-0,21x2-0,84x+50
S(x) = D(x)
2x+7,43 = -0,21x2-0,84x+50
0,21x2+2,84x-42,57=0
∆=(2,84)2-4(0,21)*(-42,57)=8,07-4*(-8,94)=8,07+35,75=43,85
√∆=6,62
X 1=
−2,84−6,62
2∗0,21
3,78
<0
3,78
X2= 2∗0,21 = 0,42 = 9
X2 is the value for which equilibrium occurs. (9)
pe = D(xe) = S(xe) = 2(9)+7,43 = 18+7,42 = 25,42
pe is the corresponding equilibrium price. (25,42)
Graph data:
D(x) = -0,21x2-0,84x+50
We need this graph only for x>0 and p>0
∆ = 0,7-4(-0,21*50) = 0,7+42 = 42,7
√∆ = 6,53
0,84−6,53
−5,69
X1= 2(−0,21) = −0,42 = 13,55
X2=
0,84+6,53
2(−0,21)
7,37
= −0,42 = -17,55
Vertex for D(x):
0,84
xv = −0,42 = -2
−42,7
−42,7
yv = 4(−0,21) = −0,84 = 50,83
S(x) = 2x+7,43