1/5x-4/5=2/3x+1

Solution for 1/5x-4/5=2/3x+1 equation:

1/5x-4/5=2/3x+1

We move all terms to the left:

1/5x-4/5-(2/3x+1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

1/5x-2/3x-1-4/5=0

We calculate fractions


3x/375x^2+(-250x)/375x^2+(-12x)/375x^2-1=0

We multiply all the terms by the denominator


3x+(-250x)+(-12x)-1*375x^2=0

Wy multiply elements

-375x^2+3x+(-250x)+(-12x)=0

We get rid of parentheses

-375x^2+3x-250x-12x=0

We add all the numbers together, and all the variables

-375x^2-259x=0

a = -375; b = -259; c = 0;
Δ = b2-4ac
Δ = -2592-4·(-375)·0
Δ = 67081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{67081}=259$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-259)-259}{2*-375}=\frac{0}{-750}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-259)+259}{2*-375}=\frac{518}{-750}
=-259/375
$