2x-2=1/2x+6

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

2x-2=1/2x+6

We move all terms to the left:

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


Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

2x-1/2x-6-2=0

We multiply all the terms by the denominator


2x*2x-6*2x-2*2x-1=0

Wy multiply elements

4x^2-12x-4x-1=0

We add all the numbers together, and all the variables

4x^2-16x-1=0

a = 4; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·4·(-1)
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{-(-16)-4\sqrt{17}}{2*4}=\frac{16-4\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{17}}{2*4}=\frac{16+4\sqrt{17}}{8}
$