2/6x-5=2x+6

Solution for 2/6x-5=2x+6 equation:

2/6x-5=2x+6

We move all terms to the left:

2/6x-5-(2x+6)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

2/6x-2x-6-5=0

We multiply all the terms by the denominator


-2x*6x-6*6x-5*6x+2=0

Wy multiply elements

-12x^2-36x-30x+2=0

We add all the numbers together, and all the variables

-12x^2-66x+2=0

a = -12; b = -66; c = +2;
Δ = b2-4ac
Δ = -662-4·(-12)·2
Δ = 4452
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:

$\sqrt{\Delta}=\sqrt{4452}=\sqrt{4*1113}=\sqrt{4}*\sqrt{1113}=2\sqrt{1113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1113}}{2*-12}=\frac{66-2\sqrt{1113}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1113}}{2*-12}=\frac{66+2\sqrt{1113}}{-24}
$