Can someone please tell me the mesh equations for the attached jpeg, I am new to this and cant get my head around it.

 

Start by drawing loops around the three enclosed square regions. Lable these loops i1, i2, & i3. (I started my labelling at the top then bottom left and then bottom right but it really doesn't matter).

As you trace away around the loops note the voltages dropped.

For example for the top-loop (i1), you get
R3*i1 + R4(i1-i3) + R2(i1-i2) = 0

(i2/i3 go against i1 and are subtracted in my loops since I have them all going CW)

Try the rest on your own and I'd be happy to review them.

 

Would the others be:

i2 = 107 + R1i2 - R2(i1-i2)

i3 = -107 - R4(i1-i3) + R5i3

 

Those look correct, except the Left Hand Sides of your equation should be set equal to zero instead of i2/i3.

 

so to solve mesh equations you:

assign loop direction in each mesh
assign voltage source in same direction as loop
assign voltage drops opposite to direction of loop
find equations of each mesh