-80/x=-40x

Solution for -80/x=-40x equation:

-80/x=-40x

We move all terms to the left:

-80/x-(-40x)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

-80/x+40x=0

We multiply all the terms by the denominator


40x*x-80=0

Wy multiply elements

40x^2-80=0

a = 40; b = 0; c = -80;
Δ = b2-4ac
Δ = 02-4·40·(-80)
Δ = 12800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12800}=\sqrt{6400*2}=\sqrt{6400}*\sqrt{2}=80\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{2}}{2*40}=\frac{0-80\sqrt{2}}{80}
=-\frac{80\sqrt{2}}{80}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{2}}{2*40}=\frac{0+80\sqrt{2}}{80}
=\frac{80\sqrt{2}}{80}
=\sqrt{2}
$