3/5x-5/6x=13/15

Solution for 3/5x-5/6x=13/15 equation:

3/5x-5/6x=13/15

We move all terms to the left:

3/5x-5/6x-(13/15)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-5/6x-(+13/15)=0

We get rid of parentheses

3/5x-5/6x-13/15=0

We calculate fractions


(-2340x^2)/450x^2+270x/450x^2+(-375x)/450x^2=0

We multiply all the terms by the denominator


(-2340x^2)+270x+(-375x)=0

We get rid of parentheses

-2340x^2+270x-375x=0

We add all the numbers together, and all the variables

-2340x^2-105x=0

a = -2340; b = -105; c = 0;
Δ = b2-4ac
Δ = -1052-4·(-2340)·0
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-105}{2*-2340}=\frac{0}{-4680}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+105}{2*-2340}=\frac{210}{-4680}
=-7/156
$