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

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

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

We move all terms to the left:

2/3x-1/5x-(-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 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
$