2(x-1)+6x=4/2x-+2

Solution for 2(x-1)+6x=4/2x-+2 equation:

2(x-1)+6x=4/2x-+2

We move all terms to the left:

2(x-1)+6x-(4/2x-+2)=0


Domain of the equation: 2x-+2)!=0

x∈R


We add all the numbers together, and all the variables

2(x-1)+6x-(+4/2x)=0

We add all the numbers together, and all the variables

6x+2(x-1)-(+4/2x)=0

We multiply parentheses

6x+2x-(+4/2x)-2=0

We get rid of parentheses

6x+2x-4/2x-2=0

We multiply all the terms by the denominator


6x*2x+2x*2x-2*2x-4=0

Wy multiply elements

12x^2+4x^2-4x-4=0

We add all the numbers together, and all the variables

16x^2-4x-4=0

a = 16; b = -4; c = -4;
Δ = b2-4ac
Δ = -42-4·16·(-4)
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{17}}{2*16}=\frac{4-4\sqrt{17}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{17}}{2*16}=\frac{4+4\sqrt{17}}{32}
$