5/6x-1/10x=2/15

Solution for 5/6x-1/10x=2/15 equation:

5/6x-1/10x=2/15

We move all terms to the left:

5/6x-1/10x-(2/15)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x-1/10x-(+2/15)=0

We get rid of parentheses

5/6x-1/10x-2/15=0

We calculate fractions


(-120x^2)/900x^2+750x/900x^2+(-90x)/900x^2=0

We multiply all the terms by the denominator


(-120x^2)+750x+(-90x)=0

We get rid of parentheses

-120x^2+750x-90x=0

We add all the numbers together, and all the variables

-120x^2+660x=0

a = -120; b = 660; c = 0;
Δ = b2-4ac
Δ = 6602-4·(-120)·0
Δ = 435600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{435600}=660$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(660)-660}{2*-120}=\frac{-1320}{-240}
=5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(660)+660}{2*-120}=\frac{0}{-240}
=0
$