110-x=1000/x

Solution for 110-x=1000/x equation:

110-x=1000/x

We move all terms to the left:

110-x-(1000/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-(+1000/x)+110=0

We add all the numbers together, and all the variables

-1x-(+1000/x)+110=0

We get rid of parentheses

-1x-1000/x+110=0

We multiply all the terms by the denominator


-1x*x+110*x-1000=0

We add all the numbers together, and all the variables

110x-1x*x-1000=0

Wy multiply elements

-1x^2+110x-1000=0

a = -1; b = 110; c = -1000;
Δ = b2-4ac
Δ = 1102-4·(-1)·(-1000)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-90}{2*-1}=\frac{-200}{-2}
=+100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+90}{2*-1}=\frac{-20}{-2}
=+10
$