x-5=100/x

Solution for x-5=100/x equation:

x-5=100/x

We move all terms to the left:

x-5-(100/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-(+100/x)-5=0

We get rid of parentheses

x-100/x-5=0

We multiply all the terms by the denominator


x*x-5*x-100=0

We add all the numbers together, and all the variables

-5x+x*x-100=0

Wy multiply elements

x^2-5x-100=0

a = 1; b = -5; c = -100;
Δ = b2-4ac
Δ = -52-4·1·(-100)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{17}}{2*1}=\frac{5-5\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{17}}{2*1}=\frac{5+5\sqrt{17}}{2}
$