2/4x-6=2x+12

Solution for 2/4x-6=2x+12 equation:

2/4x-6=2x+12

We move all terms to the left:

2/4x-6-(2x+12)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

2/4x-2x-12-6=0

We multiply all the terms by the denominator


-2x*4x-12*4x-6*4x+2=0

Wy multiply elements

-8x^2-48x-24x+2=0

We add all the numbers together, and all the variables

-8x^2-72x+2=0

a = -8; b = -72; c = +2;
Δ = b2-4ac
Δ = -722-4·(-8)·2
Δ = 5248
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:

$\sqrt{\Delta}=\sqrt{5248}=\sqrt{64*82}=\sqrt{64}*\sqrt{82}=8\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{82}}{2*-8}=\frac{72-8\sqrt{82}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{82}}{2*-8}=\frac{72+8\sqrt{82}}{-16}
$