80-x=500/x

Solution for 80-x=500/x equation:

80-x=500/x

We move all terms to the left:

80-x-(500/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-(+500/x)+80=0

We add all the numbers together, and all the variables

-1x-(+500/x)+80=0

We get rid of parentheses

-1x-500/x+80=0

We multiply all the terms by the denominator


-1x*x+80*x-500=0

We add all the numbers together, and all the variables

80x-1x*x-500=0

Wy multiply elements

-1x^2+80x-500=0

a = -1; b = 80; c = -500;
Δ = b2-4ac
Δ = 802-4·(-1)·(-500)
Δ = 4400
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:

$\sqrt{\Delta}=\sqrt{4400}=\sqrt{400*11}=\sqrt{400}*\sqrt{11}=20\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-20\sqrt{11}}{2*-1}=\frac{-80-20\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+20\sqrt{11}}{2*-1}=\frac{-80+20\sqrt{11}}{-2}
$