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

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

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

We move all terms to the left:

3/5x+2/3-(1/3x+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

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

We calculate fractions


81x/135x^2+(-5x)/135x^2+10x/135x^2-1=0

We multiply all the terms by the denominator


81x+(-5x)+10x-1*135x^2=0

We add all the numbers together, and all the variables

91x+(-5x)-1*135x^2=0

Wy multiply elements

-135x^2+91x+(-5x)=0

We get rid of parentheses

-135x^2+91x-5x=0

We add all the numbers together, and all the variables

-135x^2+86x=0

a = -135; b = 86; c = 0;
Δ = b2-4ac
Δ = 862-4·(-135)·0
Δ = 7396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7396}=86$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86)-86}{2*-135}=\frac{-172}{-270}
=86/135
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86)+86}{2*-135}=\frac{0}{-270}
=0
$