x-400=100/x

Solution for x-400=100/x equation:

x-400=100/x

We move all terms to the left:

x-400-(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)-400=0

We get rid of parentheses

x-100/x-400=0

We multiply all the terms by the denominator


x*x-400*x-100=0

We add all the numbers together, and all the variables

-400x+x*x-100=0

Wy multiply elements

x^2-400x-100=0

a = 1; b = -400; c = -100;
Δ = b2-4ac
Δ = -4002-4·1·(-100)
Δ = 160400
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:

$\sqrt{\Delta}=\sqrt{160400}=\sqrt{400*401}=\sqrt{400}*\sqrt{401}=20\sqrt{401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-20\sqrt{401}}{2*1}=\frac{400-20\sqrt{401}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+20\sqrt{401}}{2*1}=\frac{400+20\sqrt{401}}{2}
$