  We consider the equation $$ ab + cd = \lambda, \qquad a\in A, b \in B, c\in
C, d \in D, $$ over a finite field $F_q$ of $q$ elements, with variables from
arbitrary sets $ A, B, C, D \subseteq F_q$. The question of solvability of such
and more general equations has recently been considered by D. Hart and A.
Iosevich, who, in particular, proved that if $$ #A #B #C #D \gg q^3, $$ then
above equation has a solution for any $\lambda \in F_q^*$. Here we show that
using bounds of multiplicative character sums allows us to extend the class of
sets which satisfy this property.
