2/4x-4=5/6x

Solution for 2/4x-4=5/6x equation:

2/4x-4=5/6x

We move all terms to the left:

2/4x-4-(5/6x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/4x-(+5/6x)-4=0

We get rid of parentheses

2/4x-5/6x-4=0

We calculate fractions


12x/24x^2+(-20x)/24x^2-4=0

We multiply all the terms by the denominator


12x+(-20x)-4*24x^2=0

Wy multiply elements

-96x^2+12x+(-20x)=0

We get rid of parentheses

-96x^2+12x-20x=0

We add all the numbers together, and all the variables

-96x^2-8x=0

a = -96; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-96)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-96}=\frac{0}{-192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-96}=\frac{16}{-192}
=-1/12
$