1/2x+1/6=1/8x+1

Solution for 1/2x+1/6=1/8x+1 equation:

1/2x+1/6=1/8x+1

We move all terms to the left:

1/2x+1/6-(1/8x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x+1)!=0

x∈R


We get rid of parentheses

1/2x-1/8x-1+1/6=0

We calculate fractions


128x^2/576x^2+288x/576x^2+(-72x)/576x^2-1=0

We multiply all the terms by the denominator


128x^2+288x+(-72x)-1*576x^2=0

Wy multiply elements

128x^2-576x^2+288x+(-72x)=0

We get rid of parentheses

128x^2-576x^2+288x-72x=0

We add all the numbers together, and all the variables

-448x^2+216x=0

a = -448; b = 216; c = 0;
Δ = b2-4ac
Δ = 2162-4·(-448)·0
Δ = 46656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46656}=216$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-216}{2*-448}=\frac{-432}{-896}
=27/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+216}{2*-448}=\frac{0}{-896}
=0
$