Specialized numerical method for transcendental equation

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Is there any specialized, very fast, numerical method for solving equations of a type $$ e^{-px-q} = \frac{ax^2 + bx + c}{kx + l} $$ wher all $ a, p, q $ are strictly positive? To be more precise, is there anything that I could use except bisection, regula falsi, or Newton-Raphson's method? Maybe in combination with something specific?