1/2x+3=1/6x+5

Solution for 1/2x+3=1/6x+5 equation:

1/2x+3=1/6x+5

We move all terms to the left:

1/2x+3-(1/6x+5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x+5)!=0

x∈R


We get rid of parentheses

1/2x-1/6x-5+3=0

We calculate fractions


6x/12x^2+(-2x)/12x^2-5+3=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-24x^2+6x+(-2x)=0

We get rid of parentheses

-24x^2+6x-2x=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
$