104/x=x-5

Solution for 104/x=x-5 equation:

104/x=x-5

We move all terms to the left:

104/x-(x-5)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

104/x-x+5=0

We multiply all the terms by the denominator


-x*x+5*x+104=0

We add all the numbers together, and all the variables

5x-x*x+104=0

Wy multiply elements

-1x^2+5x+104=0

a = -1; b = 5; c = +104;
Δ = b2-4ac
Δ = 52-4·(-1)·104
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-21}{2*-1}=\frac{-26}{-2}
=+13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+21}{2*-1}=\frac{16}{-2}
=-8
$