It's an equilateral triangle, therefore
AB = BC = BA
We have the equation:
[tex]\dfrac{3}{2}x-12=\dfrac{1}{2}x-2\qquad\text{multiply both sides by 2}\\\\3x-24=1x-4\qquad\text{add 24 to both sides}\\\\3x=x+20\qquad\text{subtract x from both sides}\\\\2x=20\qquad\text{divide both sides by 2}\\\\x=10[/tex]
[tex]BC=BA\to BC=\dfrac{1}{2}(10)-2=5-2=3[/tex]
Answer: BC = 3
