Question

Solve that $x$ : $\frac{m}{n}{x}^2+\frac{n}{m}=1-2x$ .

Answer 1

Given,

$\frac{m}{n}{x}^2+\frac{n}{m}=1-2x$

$m^2{x}^2+n^2=mn-2mnx$

$m^2{x}^2+2mnx+n^2-mn=0$

$a=m^2,b=2mn,c=n^2-mn$

$x=\frac{-2mn\pm \sqrt{{\left(2mn\right)}^2-4m^2(n^2-mn)}}{2m^2}$

$x=\frac{-mn\pm \sqrt{m^{3}n}}{m^2}$