  A well-known theorem of Mantel states that every $n$-vertex graph with more
than $\lfloor n^2/4\rfloor $ edges contains a triangle. An interesting problem
in extremal graph theory studies the minimum number of edges contained in
triangles among graphs with a prescribed number of vertices and edges.
Erd\H{o}s, Faudree and Rousseau (1992) showed that a graph on $n$ vertices with
more than $\lfloor n^2/4\rfloor $ edges contains at least $2\lfloor n/2\rfloor
+1$ edges in triangles. Such edges are called triangular edges. In this paper,
we present a spectral version of the result of Erd\H{o}s, Faudree and Rousseau.
Using the supersaturation-stability and the spectral technique, we prove that
every $n$-vertex graph $G$ with $\lambda (G) \ge \sqrt{\lfloor n^2/4\rfloor}$
contains at least $2 \lfloor {n}/{2} \rfloor -1$ triangular edges, unless $G$
is a balanced complete bipartite graph. The method in our paper has some
interesting applications. Firstly, the supersaturation-stability can be used to
revisit a conjecture of Erd\H{o}s concerning with the booksize of a graph,
which was initially proved by Edwards (unpublished), and independently by
Khad\v{z}iivanov and Nikiforov (1979). Secondly, our method can improve the
bound on the order $n$ of a graph by dropping the condition on $n$ being
sufficiently large, which is obtained from the triangle removal lemma. Thirdly,
the supersaturation-stability can be applied to deal with the spectral extremal
graph problems on counting triangles, which was recently studied by Ning and
Zhai (2023).
