since both triangles have a right-angle, and the two angles at vertex C are also twins, thus both triangles are similar by AA, therefore,
[tex]\bf \cfrac{small}{large}\qquad \cfrac{DE}{BA}=\cfrac{EC}{CA}\implies \cfrac{7}{84}=\cfrac{x}{156-x}\implies 1092-7x=84x
\\\\\\
1092=91x\implies \cfrac{1092}{91}=x\implies 12=x\qquad \quad \qquad \boxed{AC=156-12}[/tex]
