1/2x-13/15=1/6x-1

Solution for 1/2x-13/15=1/6x-1 equation:

1/2x-13/15=1/6x-1

We move all terms to the left:

1/2x-13/15-(1/6x-1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x-1)!=0

x∈R


We get rid of parentheses

1/2x-1/6x+1-13/15=0

We calculate fractions


(-936x^2)/180x^2+90x/180x^2+(-30x)/180x^2+1=0

We multiply all the terms by the denominator


(-936x^2)+90x+(-30x)+1*180x^2=0

Wy multiply elements

(-936x^2)+180x^2+90x+(-30x)=0

We get rid of parentheses

-936x^2+180x^2+90x-30x=0

We add all the numbers together, and all the variables

-756x^2+60x=0

a = -756; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-756)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-756}=\frac{-120}{-1512}
=5/63
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-756}=\frac{0}{-1512}
=0
$