2/5x+1/4+6=2/8x

Solution for 2/5x+1/4+6=2/8x equation:

2/5x+1/4+6=2/8x

We move all terms to the left:

2/5x+1/4+6-(2/8x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/5x-(+2/8x)+6+1/4=0

We get rid of parentheses

2/5x-2/8x+6+1/4=0

We calculate fractions


320x^2/640x^2+256x/640x^2+(-160x)/640x^2+6=0

We multiply all the terms by the denominator


320x^2+256x+(-160x)+6*640x^2=0

Wy multiply elements

320x^2+3840x^2+256x+(-160x)=0

We get rid of parentheses

320x^2+3840x^2+256x-160x=0

We add all the numbers together, and all the variables

4160x^2+96x=0

a = 4160; b = 96; c = 0;
Δ = b2-4ac
Δ = 962-4·4160·0
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-96}{2*4160}=\frac{-192}{8320}
=-3/130
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+96}{2*4160}=\frac{0}{8320}
=0
$