4/2x-12=8-12/4x

Solution for 4/2x-12=8-12/4x equation:

4/2x-12=8-12/4x

We move all terms to the left:

4/2x-12-(8-12/4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/2x-(-12/4x+8)-12=0

We get rid of parentheses

4/2x+12/4x-8-12=0

We calculate fractions


16x/8x^2+24x/8x^2-8-12=0

We add all the numbers together, and all the variables

16x/8x^2+24x/8x^2-20=0

We multiply all the terms by the denominator


16x+24x-20*8x^2=0

We add all the numbers together, and all the variables

40x-20*8x^2=0

Wy multiply elements

-160x^2+40x=0

a = -160; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·(-160)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*-160}=\frac{-80}{-320}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*-160}=\frac{0}{-320}
=0
$