2/6x=6/5x+2

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

2/6x=6/5x+2

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 5x+2)!=0

x∈R


We get rid of parentheses

2/6x-6/5x-2=0

We calculate fractions


10x/30x^2+(-36x)/30x^2-2=0

We multiply all the terms by the denominator


10x+(-36x)-2*30x^2=0

Wy multiply elements

-60x^2+10x+(-36x)=0

We get rid of parentheses

-60x^2+10x-36x=0

We add all the numbers together, and all the variables

-60x^2-26x=0

a = -60; b = -26; c = 0;
Δ = b2-4ac
Δ = -262-4·(-60)·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-26}{2*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+26}{2*-60}=\frac{52}{-120}
=-13/30
$