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#.