X+679/x=104

Solution for X+679/x=104 equation:

X+679/X=104

We move all terms to the left:

X+679/X-(104)=0


Domain of the equation: X!=0

X∈R


We multiply all the terms by the denominator


X*X-104*X+679=0

We add all the numbers together, and all the variables

-104X+X*X+679=0

Wy multiply elements

X^2-104X+679=0

a = 1; b = -104; c = +679;
Δ = b2-4ac
Δ = -1042-4·1·679
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{-(-104)-90}{2*1}=\frac{14}{2}
=7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+90}{2*1}=\frac{194}{2}
=97
$