1. **State the problem:** Solve for $d$ in the equation $$-55 + 48\sqrt{d} = 89.$$\n\n2. **Isolate the square root term:** Add 55 to both sides to get $$48\sqrt{d} = 89 + 55.$$\n\n3. Simplify the right side: $$48\sqrt{d} = 144.$$\n\n4. **Divide both sides by 48:** $$\cancel{48}\sqrt{d} = \frac{144}{\cancel{48}}$$ which simplifies to $$\sqrt{d} = 3.$$\n\n5. **Square both sides to solve for $d$:** $$\left(\sqrt{d}\right)^2 = 3^2$$ which gives $$d = 9.$$\n\n6. **Final answer:** $$d = 9.$$