2x+2=16-2x/x

Solution for 2x+2=16-2x/x equation:

2x+2=16-2x/x

We move all terms to the left:

2x+2-(16-2x/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

2x-(-2x/x+16)+2=0

We get rid of parentheses

2x+2x/x-16+2=0

We multiply all the terms by the denominator


2x*x+2x-16*x+2*x=0

We add all the numbers together, and all the variables

-12x+2x*x=0

Wy multiply elements

2x^2-12x=0

a = 2; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·2·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*2}=\frac{24}{4}
=6
$