Question 848108
2*a*b+4*b*c=350
a = 1,   b = 1,   c = 87
a = 1,   b = 5,   c = 17
There are five integer solutions with a=1

There are a total of 121 integer solutions
Here are some of them
a = 3,   b = 7,   c = 11
a = 3,   b = 5,   c = 16
a = 5,   b = 5,   c = 15
a = 7,   b = 7,   c = 9
a = 7,   b = 5,   c = 14

a = 9,   b = 5,   c = 13

2*9*5=90
4*5*13=260