Question 299581
<pre><font size = 4 color = "indigo"><b>
{{{a^2 - 12a + 35 = 0}}}

Since the quadratic formula itself contains the letter a,
we must avoid confusion between the two uses for a.  
So let's use another letter besides a.  Let's substitute x
for a:

{{{x^2 - 12x + 35 = 0}}}

{{{a=1}}}, {{{b=-12}}}, {{{c=35}}}

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{x = (-(-12) +- sqrt( (-12)^2-4*(1)*(35) ))/(2*(1)) }}}

{{{x = (12 +- sqrt(144-140) )/2 }}}

{{{x = (12 +- sqrt(4) )/2 }}}

{{{x = (12 +- 2 )/2 }}}

Using the +

{{{x = (12 + 2 )/2 =14/2=7}}}

Using the -

{{{x = (12 - 2 )/2 =10/2=5}}}

There are two solutions 7 and 5

Now we switch back to a from x, and get

a = 7 and a = 5.

Edwin</pre>