2+2/4x=5-1/6x

Solution for 2+2/4x=5-1/6x equation:

2+2/4x=5-1/6x

We move all terms to the left:

2+2/4x-(5-1/6x)=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-(-1/6x+5)+2=0

We get rid of parentheses

2/4x+1/6x-5+2=0

We calculate fractions


12x/24x^2+4x/24x^2-5+2=0

We add all the numbers together, and all the variables

12x/24x^2+4x/24x^2-3=0

We multiply all the terms by the denominator


12x+4x-3*24x^2=0

We add all the numbers together, and all the variables

16x-3*24x^2=0

Wy multiply elements

-72x^2+16x=0

a = -72; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-72)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-72}=\frac{-32}{-144}
=2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-72}=\frac{0}{-144}
=0
$