Delay Differential Equations (DDEs) are used to model many systems in medicine, chemistry, and environmental science, and are characterized by the derivative of the function being dependent on the solution in both the present and the past. They are utilized in realistic systems where the transfer between states is not instantaneous, or there is delayed activation of some component. While much literature has been focused on creating quantum algorithms for ODEs, there is no such research considering DDEs. We extend the method of solving lin ear delay functions as a matrix equation to first-order DDEs by creating custom quantum block-encoding oracles for the coefficient matrix resulting from both constant and variable-delays. The findings now allow this new class of equations to be solved faster than linear time with quantum linear system solvers.