How De Broglie's wavelength found/derived?

Through energy conservation, we can determine that no energy is lost and thereforeKinetic energy = Electrical energyAs a result the following equation is present where both sides represent energy:(m*(v^2))/2 = eVHere: ·        m = the mass of the electron·        v = the speed of the electron·        e = charge on a single electron·        V = voltageBy multiplying both formulae by (m/m) or 1, we can derive the following equations:((mv)^2)/(2m) = eV(p^2)/(2m) = eVHere, p = the momentum of the electronWe also know another equation for energy that leads us to determine:Energy = (hc)/ λ = m(c^2)Here: ·        h = Planck’s constant·        c = the speed of light·        λ = De Broglie’s wavelengthBy cancelling out c from both sides of the equation we can arrive at the equations:h/λ = mch/λ = pWe then substitute this into the earlier equation to arrive at the following:h^2/(2m*(λ^2)) = eV(2m*(λ^2))/h^2 = 1/(eV)(λ^2) = (h^2)/(2meV)λ = h/((2me*V)^(1/2))The final equation represents De Broglie’s wavelength.