2-2/4x=5/6x+8

Solution for 2-2/4x=5/6x+8 equation:

2-2/4x=5/6x+8

We move all terms to the left:

2-2/4x-(5/6x+8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x+8)!=0

x∈R


We get rid of parentheses

-2/4x-5/6x-8+2=0

We calculate fractions


(-12x)/24x^2+(-20x)/24x^2-8+2=0

We add all the numbers together, and all the variables

(-12x)/24x^2+(-20x)/24x^2-6=0

We multiply all the terms by the denominator


(-12x)+(-20x)-6*24x^2=0

Wy multiply elements

-144x^2+(-12x)+(-20x)=0

We get rid of parentheses

-144x^2-12x-20x=0

We add all the numbers together, and all the variables

-144x^2-32x=0

a = -144; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-144)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-144}=\frac{0}{-288}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-144}=\frac{64}{-288}
=-2/9
$