3/8x+1=1/6x

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Solution for 3/8x+1=1/6x equation: 



3/8x+1=1/6x

We move all terms to the left:

3/8x+1-(1/6x)=0



Domain of the equation: 8x!=0

x!=0/8

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

3/8x-(+1/6x)+1=0

We get rid of parentheses

3/8x-1/6x+1=0

We calculate fractions


18x/48x^2+(-8x)/48x^2+1=0

We multiply all the terms by the denominator


18x+(-8x)+1*48x^2=0

Wy multiply elements

48x^2+18x+(-8x)=0

We get rid of parentheses

48x^2+18x-8x=0

We add all the numbers together, and all the variables

48x^2+10x=0

a = 48; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·48·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*48}=\frac{-20}{96}
=-5/24
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*48}=\frac{0}{96}
=0
$

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