5/3x-7/5=1/6x

Solution for 5/3x-7/5=1/6x equation:

5/3x-7/5=1/6x

We move all terms to the left:

5/3x-7/5-(1/6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/3x-(+1/6x)-7/5=0

We get rid of parentheses

5/3x-1/6x-7/5=0

We calculate fractions


(-756x^2)/450x^2+750x/450x^2+(-75x)/450x^2=0

We multiply all the terms by the denominator


(-756x^2)+750x+(-75x)=0

We get rid of parentheses

-756x^2+750x-75x=0

We add all the numbers together, and all the variables

-756x^2+675x=0

a = -756; b = 675; c = 0;
Δ = b2-4ac
Δ = 6752-4·(-756)·0
Δ = 455625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{455625}=675$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(675)-675}{2*-756}=\frac{-1350}{-1512}
=25/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(675)+675}{2*-756}=\frac{0}{-1512}
=0
$