12/2x+4=4x+12

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

12/2x+4=4x+12

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2-24x+8x+12=0

We add all the numbers together, and all the variables

-8x^2-16x+12=0

a = -8; b = -16; c = +12;
Δ = b2-4ac
Δ = -162-4·(-8)·12
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{10}}{2*-8}=\frac{16-8\sqrt{10}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{10}}{2*-8}=\frac{16+8\sqrt{10}}{-16}
$