120/80*x-x=0

Solution for 120/80*x-x=0 equation:

120/80x-x=0


Domain of the equation: 80x!=0

x!=0/80

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+120/80x=0

We multiply all the terms by the denominator


-1x*80x+120=0

Wy multiply elements

-80x^2+120=0

a = -80; b = 0; c = +120;
Δ = b2-4ac
Δ = 02-4·(-80)·120
Δ = 38400
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:

$\sqrt{\Delta}=\sqrt{38400}=\sqrt{6400*6}=\sqrt{6400}*\sqrt{6}=80\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{6}}{2*-80}=\frac{0-80\sqrt{6}}{-160}
=-\frac{80\sqrt{6}}{-160}
=-\frac{\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{6}}{2*-80}=\frac{0+80\sqrt{6}}{-160}
=\frac{80\sqrt{6}}{-160}
=\frac{\sqrt{6}}{-2}
$