Solve[21q-q^2 -10==0,q]

N[%]

{{q->0.48750780274960626`},{q->20.512492197250396`}}

alpha =38
C1=1
C2=6
Solve [Q1 == (alpha-C1)/2 -  (alpha-C2)/4+Q1/4, Q1  ]

{{Q1->14}}
Q2=  (alpha-C2)/2 - Q1/2