I'm not 100% sure about this. But I think this will help you.
Let's think if one article's cost is y
Then 2x articles cost,
2xy = 5x+54
and (x+2) articles cost,
(x+2)y = 10x-4
Let's devide both equations,
2x/(x+2) = (5x+54)/(10x-4)
2x(10x-4) = (x+2)(5x+54)
20x² - 8x = 5x² + 54x + 10x + 108
15x² - 72x - 108 = 0
3x² - 24x - 36 = 0
3x² - 18x - 6x - 36 = 0
3x(x-6) - 6(x-6) =0
(3x-6)(x-6)=0
So 3x-6 = 0 or x-6 = 0
So x = 2 or x=6