2/3x+1/5=6-1/5x

Solution for 2/3x+1/5=6-1/5x equation:

2/3x+1/5=6-1/5x

We move all terms to the left:

2/3x+1/5-(6-1/5x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(-1/5x+6)+1/5=0

We get rid of parentheses

2/3x+1/5x-6+1/5=0

We calculate fractions


250x/375x^2+3x/375x^2+3x/375x^2-6=0

We multiply all the terms by the denominator


250x+3x+3x-6*375x^2=0

We add all the numbers together, and all the variables

256x-6*375x^2=0

Wy multiply elements

-2250x^2+256x=0

a = -2250; b = 256; c = 0;
Δ = b2-4ac
Δ = 2562-4·(-2250)·0
Δ = 65536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{65536}=256$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(256)-256}{2*-2250}=\frac{-512}{-4500}
=128/1125
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(256)+256}{2*-2250}=\frac{0}{-4500}
=0
$