Why are there two contradicting formulas for Enthalpy (Delta H):
This is my take on this


  1) Delta H = Bonds broken - Bonds Formed
  
  2) Delta H = $H_{products}−H_{reactants}$


Equation 2 is pretty straightforward, (change in enthalpy is the enthalpy of the products minus the enthalphy of the reactants).

Equation 1 is a bit less straightforward. Let's define the system as where you are having the reaction, and the surroundings as everything else. When you break bonds, you take energy from the surroundings into the system. Then, when bonds are formed, energy is released from the system into the surroundings. Therefore, if there is more energy released in the bonds formed than there is energy gained in the bonds broken, the system loses energy. How I see it is, you are looking from the surrounding's perspective at equation 1 and from the system's perspective from equation 2, that's why you got two opposite statements (from your POV).