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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


75x^2/225x^2+(-75x)/225x^2+90x/225x^2=0

We multiply all the terms by the denominator


75x^2+(-75x)+90x=0

We add all the numbers together, and all the variables

75x^2+90x+(-75x)=0

We get rid of parentheses

75x^2+90x-75x=0

We add all the numbers together, and all the variables

75x^2+15x=0

a = 75; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·75·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*75}=\frac{-30}{150}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*75}=\frac{0}{150}
=0
$