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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

253x+(-12x)-1*375x^2=0

Wy multiply elements

-375x^2+253x+(-12x)=0

We get rid of parentheses

-375x^2+253x-12x=0

We add all the numbers together, and all the variables

-375x^2+241x=0

a = -375; b = 241; c = 0;
Δ = b2-4ac
Δ = 2412-4·(-375)·0
Δ = 58081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{58081}=241$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(241)-241}{2*-375}=\frac{-482}{-750}
=241/375
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(241)+241}{2*-375}=\frac{0}{-750}
=0
$