4/6x+1=2/4x

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

4/6x+1=2/4x

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

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

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

We get rid of parentheses

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

We calculate fractions


16x/24x^2+(-12x)/24x^2+1=0

We multiply all the terms by the denominator


16x+(-12x)+1*24x^2=0

Wy multiply elements

24x^2+16x+(-12x)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

24x^2+4x=0

a = 24; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·24·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*24}=\frac{-8}{48}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*24}=\frac{0}{48}
=0
$