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You'll find "real-life applications" of the quadratic equation mainly in engineering applications, not in sustainable development.
The quadratic equation has multiple real-world applications throughout engineering. One of which is modeling ballistic arcs and trajectories as in the path of bullet or projectile.
A differential equation is a measure of change. If differencing with respect to time, it is the rate of change. Location, when differentiated, gives velocity. Velocity, when differentiated, gives acceleration. There are significant applications across all aspects of science.
All the optimization problems in Computer Science have a predecessor analogue in continuous domain and they are generally expressed in the form of either functional differential equation or partial differential equation. A classic example is the Hamiltonian Jacobi Bellman equation which is the precursor of Bellman Ford algorithm in CS.