For parabolic equations, finding solutions to the equations can be done by two ways:
(1) Finding multiplicative factors of the constant or the rightmost term (i.e. -609) that add up to the numerical value of the middle term (-8). This method is recommended if the rightmost term doesn't have much factors. This would be difficult if the rightmost term were rational with several possible factors. Furthermore, this method requires a bit of a trail-and-error.
After multiple attempts of trial-and-error, I have found that
(x+21)(x-29)=0
Wherein 609 is the product of factors -29 and 21 and consequently the sum of these two factors is -8.
(2) The quadratic equation.
The quadratic equation is x=frac(-b+-\sqrt(b^2-4ac))(2a).
So what are the variables a,b, and c? These are just the numerical values of each term in the quadratic equation.
Specifically;
a corresponds to the numerical value of the leftmost term;
b corresponds to the numerical value of the middle term; and
c corresponds to the numerical value of the rightmost term.
From the original equation,
a=1
b=-8
c=-609
Then, plug-in these values into the quadratic equation:
(i) x=frac(-(-8)+\sqrt((-8)^2-(4)(1)(-609)))(2(1))=29
(ii) x=frac(-(-8)-\sqrt((-8)^2-(4)(1)(-609)))(21)=-21
Therefore,
From the obtained x values, the factors should
(x+21)(x-29)=0
to maintain the equality of the right side of the equation, 0.