Apply using the following theory:

Assume an elastic collision:

initial KE = 1/2 m1 v1^2
=
final KE = 1/2 m1 v1f^2 + 1/2 m2 v2f^2

initial momentum = m1 v1
=
final momentum = m1 v1f + m2 v2f

Two equations, two unknowns

Solve the second equation for the second marble’s speed after collision:
v2f = m1 (v1 – v1f) /m2

Plug that into the first:
m2 v1^2 = m2 v1f^2 + m1 (v1 – v1f)^2

0 = v1f^2 (m2 + m1) – 2 m1 v1 vf – v1^2 (m2 – m1)

And solve the quadratic for v1f

v1f = 2 m1 v1 +- sqrt (4m1^2 v1^2 + 4 v1^2 (m2^2 – m1^2) ) / 2 (m2+m1)

= v1 (m1 +- m2) / (m2 + m1)

= v1 or v1 (m1 – m2) / (m1 + m2)

The first solution means it just went through without touching the other marble.

The second one is the one you want.

And substitute to get the final speed of the second ball:
v2f = m1 (v1 – v1f) /m2
= 2 m1 v1 / (m1 + m2)