10/x+4x=110/x

Solution for 10/x+4x=110/x equation:

10/x+4x=110/x

We move all terms to the left:

10/x+4x-(110/x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10/x+4x-(+110/x)=0

We add all the numbers together, and all the variables

4x+10/x-(+110/x)=0

We get rid of parentheses

4x+10/x-110/x=0

We multiply all the terms by the denominator


4x*x+10-110=0

We add all the numbers together, and all the variables

4x*x-100=0

Wy multiply elements

4x^2-100=0

a = 4; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·4·(-100)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40}{2*4}=\frac{-40}{8}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40}{2*4}=\frac{40}{8}
=5
$