Question 1101649
<pre>
{{{1+3^""/x^""}}}{{{""=""}}}{{{28^""/x^2}}}

Multiply through by x<sup>2</sup>

{{{x^2+3x}}}{{{""=""}}}{{{28}}}

Multiply 3 by {{{1/2}}}, get {{{3/2}}}
Square {{{3/2}}}, get {{{9/4}}}
Add {{{9/4}}} to both sides:

{{{x^2+3x+9/4}}}{{{""=""}}}{{{28+9/4}}}

Factor the left side:
Get LCD of 4 on the right side:

{{{(x+3/2)(x+3/2)}}}{{{""=""}}}{{{28*expr(4/4)+9/4}}}

Write the left side as the square of a binomial since 
both factors are the same.
Multiply the 28 by the numerator 4 on the right side.

{{{(x+3/2)^2}}}{{{""=""}}}{{{112/4+9/4}}}

Finish combining the right side:

{{{(x+3/2)^2}}}{{{""=""}}}{{{121/4}}}

Take square roots of both sides, remembering ±
on the right side.

{{{sqrt((x+3/2)^2)}}}{{{""=""}}}{{{"" +- sqrt(121/4)}}}

{{{x+3/2}}}{{{""=""}}}{{{"" +- 11/2}}}

Use the + on the right

{{{x+3/2}}}{{{""=""}}}{{{11/2}}}

Subtract {{{3/2}}} from both sides:

{{{x}}}{{{""=""}}}{{{11/2-3/2}}} 

{{{x}}}{{{""=""}}}{{{8/2}}}

{{{x}}}{{{""=""}}}{{{4}}}  <-- that's one solution.

Go back to 

{{{x+3/2}}}{{{""=""}}}{{{"" +- 11/2}}}

Use the - on the right

{{{x+3/2}}}{{{""=""}}}{{{-11/2}}}

Subtract {{{3/2}}} from both sides:

{{{x}}}{{{""=""}}}{{{-11/2-3/2}}} 

{{{x}}}{{{""=""}}}{{{-14/2}}}

{{{x}}}{{{""=""}}}{{{-7}}}  <-- that's the other solution.

The solution set is {-7,4}

Edwin</pre>