mathematical adjustment (IRR)

Question

Is here anybody who can help me with mathematical adjustment between equation 8 and 9 in the picture?

Ignore the text between equations

Answer 1

This is an instance of completing the square.

Note that $$(x-\frac{CF_1}{2CF_2})^2 = x^2 - \frac{CF_1}{CF_2}x + \frac{CF_1^2}{4CF_2^2}$$

Recognize that the right hand side of this equation is just the right hand side of $(8)$ + $\frac{CF_1^2}{4CF_2^2}$.

Thus if you add $\frac{CF_1^2}{4CF_2^2}$ to both sides of the equation in $(8)$, you get that $$\frac{y - CF_0}{CF_2} + \frac{CF_1^2}{4CF_2^2} = (x-\frac{CF_1}{2CF_2})^2$$ which gets you to $(9)$ after multiplying by $CF_2$.

Answer 2

It looks like they used the quadratic formula...