20+4x=100/x

Solution for 20+4x=100/x equation:

20+4x=100/x

We move all terms to the left:

20+4x-(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

4x-(+100/x)+20=0

We get rid of parentheses

4x-100/x+20=0

We multiply all the terms by the denominator


4x*x+20*x-100=0

We add all the numbers together, and all the variables

20x+4x*x-100=0

Wy multiply elements

4x^2+20x-100=0

a = 4; b = 20; c = -100;
Δ = b2-4ac
Δ = 202-4·4·(-100)
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20\sqrt{5}}{2*4}=\frac{-20-20\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20\sqrt{5}}{2*4}=\frac{-20+20\sqrt{5}}{8}
$