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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


6x/15x^2+(-5x)/15x^2-6+2=0

We add all the numbers together, and all the variables

6x/15x^2+(-5x)/15x^2-4=0

We multiply all the terms by the denominator


6x+(-5x)-4*15x^2=0

Wy multiply elements

-60x^2+6x+(-5x)=0

We get rid of parentheses

-60x^2+6x-5x=0

We add all the numbers together, and all the variables

-60x^2+x=0

a = -60; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-60)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-60}=\frac{-2}{-120}
=1/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-60}=\frac{0}{-120}
=0
$