x+18/x=100

Solution for x+18/x=100 equation:

x+18/x=100

We move all terms to the left:

x+18/x-(100)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-100*x+18=0

We add all the numbers together, and all the variables

-100x+x*x+18=0

Wy multiply elements

x^2-100x+18=0

a = 1; b = -100; c = +18;
Δ = b2-4ac
Δ = -1002-4·1·18
Δ = 9928
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:

$\sqrt{\Delta}=\sqrt{9928}=\sqrt{4*2482}=\sqrt{4}*\sqrt{2482}=2\sqrt{2482}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2482}}{2*1}=\frac{100-2\sqrt{2482}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2482}}{2*1}=\frac{100+2\sqrt{2482}}{2}
$