Solve for d
d=\frac{11-q-q^{2}}{3}
Solve for q
q=\frac{\sqrt{45-12d}-1}{2}
q=\frac{-\sqrt{45-12d}-1}{2}\text{, }d\leq \frac{15}{4}
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q^{2}-4+3d=7-q
Subtract q from both sides.
-4+3d=7-q-q^{2}
Subtract q^{2} from both sides.
3d=7-q-q^{2}+4
Add 4 to both sides.
3d=11-q-q^{2}
Add 7 and 4 to get 11.
\frac{3d}{3}=\frac{11-q-q^{2}}{3}
Divide both sides by 3.
d=\frac{11-q-q^{2}}{3}
Dividing by 3 undoes the multiplication by 3.
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