(2)/(3)x-(1)/(5)x=(14)/(15)

Solution for (2)/(3)x-(1)/(5)x=(14)/(15) equation:

(2)/(3)x-(1)/(5)x=(14)/(15)

We move all terms to the left:

(2)/(3)x-(1)/(5)x-((14)/(15))=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-1/5x-(+14/15)=0

We get rid of parentheses

2/3x-1/5x-14/15=0

We calculate fractions


(-1050x^2)/225x^2+150x/225x^2+(-45x)/225x^2=0

We multiply all the terms by the denominator


(-1050x^2)+150x+(-45x)=0

We get rid of parentheses

-1050x^2+150x-45x=0

We add all the numbers together, and all the variables

-1050x^2+105x=0

a = -1050; b = 105; c = 0;
Δ = b2-4ac
Δ = 1052-4·(-1050)·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*-1050}=\frac{-210}{-2100}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+105}{2*-1050}=\frac{0}{-2100}
=0
$