Cubic equations are foundational in engineering and science, yet conventional solution methods—such as Cardano’s formula and Lagrange’s resolvent—are often computationally complex, numerically unstable or difficult to generalize. To address these limitations, this article introduced a novel Derivative Method (D-Method) for solving cubic equations by systematically reducing them to quadratic forms via derivative-based substitutions. The D-Method provided a closed-form solution for deriving at least one real root of any cubic equation, combining simplicity, accuracy and broad applicability to equations with real or complex coefficients. Unlike classical approaches, the method avoided intricate algebraic manipulations and memorization of cumbersome formulas, streamlining both manual and computational solving. Comparative analysis demonstrated that the D-Method outperformed traditional techniques in efficiency and accessibility. The solution’s validity was rigorously proved mathematically and illustrated through numerical examples. Furthermore, the method’s underlying framework suggested potential extensions to higher-degree polynomial equations, offering a pathway for future research.

All viruses are protected by a durable protein shell regulating many crucial functions, such as host-cell infiltration and replication. Some disinfectants operate to disrupt or destroy this shell, rendering the virus inactive. However, many widely used antiviral solutions are also harmful to the environment and over prolonged usage, can be toxic to people or other desired organisms. Especially within enclosed environments, safer alternatives are necessary. This manuscript investigates the mechanisms behind CAGE, an ionic liquid that was previously identified to demonstrate antimicrobial properties and its interactions with a viral capsid protein. To do this, molecular dynamics simulations were used to simulate interactions between all the atoms involved in this process. Molecular dynamics simulations are a type of atomic-scale simulation based on computationally solving Newton’s laws of motion. The results showed that, on average, CAGE promotes certain forms of protein structure in regions of the viral protein vital for function, suggesting a mechanism for possible antimicrobial effects.