3/x+x=19/x

Solution for 3/x+x=19/x equation:

3/x+x=19/x

We move all terms to the left:

3/x+x-(19/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

3/x+x-(+19/x)=0

We add all the numbers together, and all the variables

x+3/x-(+19/x)=0

We get rid of parentheses

x+3/x-19/x=0

We multiply all the terms by the denominator


x*x+3-19=0

We add all the numbers together, and all the variables

x*x-16=0

Wy multiply elements

x^2-16=0

a = 1; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·1·(-16)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*1}=\frac{8}{2}
=4
$