can someone also explain to me why this (see photo) thanks you

 

The voltage at the top node of 5V voltage source is 5V (with ground reference). So, the current through the 2 ohms resistor
i1 = (v1 - 5)/2.
Similarly, the voltage at the top node of 3V is -3V (with ground reference). So, the current through the 4 ohms resistor
i3 = (v1 - (-3V))/4 = (v1 + 3)/4.

 

please let me know if the current vector was towards the node (i mean know kircoff equation is -i1+i2-i3=0 if it was i1+i2-i3=0) then it would be the same or not? thank you

 

Sorry, I am not sure if I understand your question.

If all current directions are reverse as shown in the picture, then the Kirchhoff's Current Law for the top node is i1 + i2 + i3 = 0. However, i1, i2 and i3 now will be a bit different.
See the picture.

BTW, you can choose the current in any direction you want but after that you need to express in in terms of node voltage correctly and the result should be same for v1.

 

Here is another way:

 

i can not thank you enought thank you