5/6x=4/2x+4

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

5/6x=4/2x+4

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


10x/12x^2+(-24x)/12x^2-4=0

We multiply all the terms by the denominator


10x+(-24x)-4*12x^2=0

Wy multiply elements

-48x^2+10x+(-24x)=0

We get rid of parentheses

-48x^2+10x-24x=0

We add all the numbers together, and all the variables

-48x^2-14x=0

a = -48; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-48)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*-48}=\frac{0}{-96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-48}=\frac{28}{-96}
=-7/24
$