Question 1058267
<pre><font size = 4 color = "indigo"><b>

{{{9x^2+6x=8}}}

Divide thru by 9, the coefficient of the 
term in {{{x^2}}}

{{{(9/9)x^2+(6/9)x=8/9}}}

{{{x^2+(2/3)x=8/9}}}

To the side, multiply the coefficient of x by {{{1/2}}}.
{{{(2/3)(1/2)=1/3}}}

Now square {{{1/3}}}.  {{{(1/3)^2=1/9}}}

Add {{{1/9}}} to both sides of

{{{x^2+(2/3)x+1/9=8/9+1/9}}}

Combine the right side: {{{8/9+1/9=9/9=1}}}

{{{x^2+(2/3)x+1/9=1}}}

Factor the left side:

{{{(x+1/3)(x+1/3)=1}}}

Write the left side as the square of
a binomial:

{{{(x+1/3)^2=1}}}

Take the square root of both sides,
remembering the ± on the right:

{{{sqrt((x+1/3)^2) = "" +-sqrt(1)}}}

{{{x+1/3 = "" +- 1}}}

{{{x=-1/3 +- 1}}}

Using the +

{{{x=-1/3 + 1}}}
{{{x=-1/3 + 3/3}}}
{{{x=2/3}}}

Using the -

{{{x=-1/3 - 1}}}
{{{x=-1/3 - 3/3}}}
{{{x=-4/3}}}

The solutions are {{{2/3}}} and {{{-4/3}}}

Edwin</pre>