85-x=115/x

Solution for 85-x=115/x equation:

85-x=115/x

We move all terms to the left:

85-x-(115/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-(+115/x)+85=0

We add all the numbers together, and all the variables

-1x-(+115/x)+85=0

We get rid of parentheses

-1x-115/x+85=0

We multiply all the terms by the denominator


-1x*x+85*x-115=0

We add all the numbers together, and all the variables

85x-1x*x-115=0

Wy multiply elements

-1x^2+85x-115=0

a = -1; b = 85; c = -115;
Δ = b2-4ac
Δ = 852-4·(-1)·(-115)
Δ = 6765
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-\sqrt{6765}}{2*-1}=\frac{-85-\sqrt{6765}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+\sqrt{6765}}{2*-1}=\frac{-85+\sqrt{6765}}{-2}
$