Question 402303
{{{3}}}{{{""=""}}}{{{5/x}}}{{{""+""}}}{{{4/x^2}}}
<pre><font face = "batangche" color = "indigo" size = 4><b>

Multiply through by LCD = x² to clear of fractions


{{{red(x^2)*3}}}{{{""=""}}}{{{red(x^2)*expr(5/x)}}}{{{""+""}}}{{{red(x^2)*expr(4/x^2)}}}

{{{3x^2}}}{{{""=""}}}{{{red(x^cross(2))*expr(5/cross(x))}}}{{{""+""}}}{{{red(cross(x^2))*expr(4/cross(x^2))}}}

{{{3x^2}}}{{{""=""}}}{{{5x}}}{{{""+""}}}{{{4}}}

Get 0 on the right and the left in descending order:

{{{3x^2}}}{{{""-""}}}{{{5x}}}{{{""-""}}}{{{4}}}{{{""=""}}}{{{0}}}

Compare that to:

{{{ax^2}}}{{{""+""}}}{{{bx}}}{{{""+""}}}{{{c}}}{{{""=""}}}{{{0}}}

and we see that

{{{a=3}}}, {{{b=-5}}}, {{{c=-4}}}

So we substitute in:

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

{{{x = (-(-5) +- sqrt((-5)^2-4*(3)*(-4) ))/(2*(3)) }}}

{{{x = (5 +- sqrt(25+48))/6 }}}
 
{{{x = (5 +- sqrt(73))/6 }}}

Edwin</pre>