Question 1207661
<pre>   
{{{2x^(-2) - 3x^(-1) - 4 }}}{{{""=""}}}{{{ 0}}}

You can jump right in with the quadratic equation,
solving for x<sup>-1</sup>, the reciprocal:

 {{{x^(-1) }}}{{{""=""}}}{{{ (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

 {{{x^(-1) }}}{{{""=""}}}{{{ (-(-3) +- sqrt((-3)^2-4*2*(-4) ))/(2*(-2)) }}}

 {{{x^(-1) }}}{{{""=""}}}{{{ (3 +- sqrt(41))/4 }}}

Take reciprocals of both sides:

 {{{x }}}{{{""=""}}}{{{ 4/(3 +- sqrt(41))}}}

Then rationalize the denominator:

Using the +

{{{x }}}{{{""=""}}}{{{ matrix(1,3,4/(3 + sqrt(41)),""*"",(3 - sqrt(41))/(3 - sqrt(41)  ))}}} 

{{{x }}}{{{""=""}}}{{{ 4(3-sqrt(41))/(9-41)}}}{{{""=""}}}{{{4(3-sqrt(41))/(-32)}}}{{{""=""}}}{{{(-(3-sqrt(41)))/8}}}{{{""=""}}}{{{(-3+sqrt(41))/8}}}

Using the -, similarly {{{x }}}{{{""=""}}}{{{(-3-sqrt(41))/8}}}

Edwin</pre>