Since Angles B and C are equal, the sides AB and AC must also be equal, so you can set the equations equal to each other and solve for x. Then to find the length of BC, x can be plugged into the equation for that side length.
4x+4=6x-14
Add fourteen to each side to get x alone on the right side
4x+4+14=6x-14+14
4x+18=6x
Subtract 4x from each side to get all of the x's on one side of the equation
4x+18-4x=6x-4x
18=2x
Divide each side by two to find the value of one x
18/2=2x/2
9=x
Now that you know x equals 9, plug that into the equation for side length BC:
2x+7
2(9)+7
Multiply 2 by 9 to get rid of the parentheses
18+7
Add to simplify
25
The side of the triangle, BC, equals 25
Green is 50 and the blue is 30 degrees
