We are given one 60 degree angle, and we know that the other two angles are congruent. Since a triangle's angles add up to 180, this means that the other angles are also 60 degrees because:
180 - 60 = 120
120 / 2 = 60
The sides of an equilateral triangles are equal, so 2x+5 = 6x-7
2x + 5 - (2x) + (7) = 6x - 7 - (2x) + (7)
12 = 4x
x = 3