Solvable extensions of the naturally graded quasi-filiform Leibniz algebra of second type ${\mathcal{L}}^2$

For a sequence of the naturally graded quasi-filiform Leibniz algebra of second type ${\mathcal{L}}^2$ introduced by Camacho, G'{o}mez, Gonz'{a}lez and Omirov, all possible right and left solvable indecomposable extensions over the field $\mathbb{R}$ are constructed so that the algebra serves as the nilradical of the corresponding solvable Leibniz algebras we find in the paper.