4x+2=2/x

Solution for 4x+2=2/x equation:

4x+2=2/x

We move all terms to the left:

4x+2-(2/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-(+2/x)+2=0

We get rid of parentheses

4x-2/x+2=0

We multiply all the terms by the denominator


4x*x+2*x-2=0

We add all the numbers together, and all the variables

2x+4x*x-2=0

Wy multiply elements

4x^2+2x-2=0

a = 4; b = 2; c = -2;
Δ = b2-4ac
Δ = 22-4·4·(-2)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*4}=\frac{4}{8}
=1/2
$