2/8x+5=1/6x

Solution for 2/8x+5=1/6x equation:

2/8x+5=1/6x

We move all terms to the left:

2/8x+5-(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

2/8x-(+1/6x)+5=0

We get rid of parentheses

2/8x-1/6x+5=0

We calculate fractions


12x/48x^2+(-8x)/48x^2+5=0

We multiply all the terms by the denominator


12x+(-8x)+5*48x^2=0

Wy multiply elements

240x^2+12x+(-8x)=0

We get rid of parentheses

240x^2+12x-8x=0

We add all the numbers together, and all the variables

240x^2+4x=0

a = 240; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·240·0
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*240}=\frac{-8}{480}
=-1/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*240}=\frac{0}{480}
=0
$