The secular equations

are transformed to obtain an equation with coefficient c_A on the left and c_B on the right side. If we divide we find that

or the quadratic equation

which is equivalent to α−E_1/2 = ±(β−E_1/2S). The solutions for E₁ and E₂ are

If we insert the solution E = (&alpha+&beta)/(S+1) into the secular equation, we get

If this equation is multiplied with 1+S we get

which is true for

In the same way, we insert E = (&alpha-&beta)/(S-1) into the secular equation and obtain a second pair of coefficients