I need to apply one Laplace transform formula while I have no idea how to prove it: $$\int_0^\infty e^{-st} e^{a k} e^{a^2 t} \operatorname{erfc} \left( a \sqrt{t} + \frac{k}{2 \sqrt{t}} \right) dt = \frac{e^{-k \sqrt{s}}}{\sqrt{s} (\sqrt{s}+a)}, \quad k>0 \land a \in \mathbb{C}, $$ where $\operatorname{erfc}(t) = \frac{2}{\sqrt{\pi}} \int_t^\infty e^{-x^2} dx$.
Could anyone help me with it? Thanks in advance.