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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


54x/135x^2+(-5x)/135x^2+(-5x)/135x^2-2=0

We multiply all the terms by the denominator


54x+(-5x)+(-5x)-2*135x^2=0

Wy multiply elements

-270x^2+54x+(-5x)+(-5x)=0

We get rid of parentheses

-270x^2+54x-5x-5x=0

We add all the numbers together, and all the variables

-270x^2+44x=0

a = -270; b = 44; c = 0;
Δ = b2-4ac
Δ = 442-4·(-270)·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-44}{2*-270}=\frac{-88}{-540}
=22/135
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+44}{2*-270}=\frac{0}{-540}
=0
$