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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


(-288x^2)/432x^2+162x/432x^2+(-72x)/432x^2+6=0

We multiply all the terms by the denominator


(-288x^2)+162x+(-72x)+6*432x^2=0

Wy multiply elements

(-288x^2)+2592x^2+162x+(-72x)=0

We get rid of parentheses

-288x^2+2592x^2+162x-72x=0

We add all the numbers together, and all the variables

2304x^2+90x=0

a = 2304; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·2304·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*2304}=\frac{-180}{4608}
=-5/128
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*2304}=\frac{0}{4608}
=0
$