 Homework Statement

Object A is at X=0m. Beginning at a time 0 s, A accelerates from rest at 2 m/s^2 in the positive xdirection. Object B is at X = 50 m at t = 0s and begins moving towards A from rest with an acceleration of magnitude 4m/s^2.
Part A) Where do A and B meet?
Part B) How fast is A moving when they meet?
 Homework Equations

Xf = xi + vi(t)+1/2(a)(t^2)
Vf = Vi+a(t)
Part A)
So, I set the two positions equations of A and B equal to each other since the position has to be the same.
A: 0 + 0 + 1/2(2)t^2 = 50 + 0 + 1/2(4)t^2 :B
I know I have to solve for time t, but there's no way to solve it with both sides having t^2 so im not sure which variables I got wrong for the objects.
So, I set the two positions equations of A and B equal to each other since the position has to be the same.
A: 0 + 0 + 1/2(2)t^2 = 50 + 0 + 1/2(4)t^2 :B
I know I have to solve for time t, but there's no way to solve it with both sides having t^2 so im not sure which variables I got wrong for the objects.