Final answer:
The question involves finding the break-in point of a unity feedback system's open loop transfer function, using control system techniques such as the Routh-Hurwitz criterion, although the question does not provide complete information for a precise solution.
Step-by-step explanation:
The student is asking about finding the break-in point of a unity feedback system with a given open loop transfer function HG(s) = K(s−10)(s−20) / s²+4s+8. In control systems engineering, the break-in point is found by drawing the root locus plot and identifying points where the root locus branches break away from the real axis. Although the problem does not include all the information needed to provide an exact answer, the process generally involves using techniques such as the Routh-Hurwitz criterion or calculating the derivative of the characteristic equation and setting it to zero to solve for s.
However, there seems to be some confusion in the way the question is posed. It's important to note that the provided expressions related to chemistry equations, the quadratic formula, or other unrelated engineering concepts do not apply to solving for the break-in point in the context of a unity feedback system.