3/5x-8/15x=1/10

Solution for 3/5x-8/15x=1/10 equation:

3/5x-8/15x=1/10

We move all terms to the left:

3/5x-8/15x-(1/10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-8/15x-(+1/10)=0

We get rid of parentheses

3/5x-8/15x-1/10=0

We calculate fractions


(-75x^2)/750x^2+450x/750x^2+(-400x)/750x^2=0

We multiply all the terms by the denominator


(-75x^2)+450x+(-400x)=0

We get rid of parentheses

-75x^2+450x-400x=0

We add all the numbers together, and all the variables

-75x^2+50x=0

a = -75; b = 50; c = 0;
Δ = b2-4ac
Δ = 502-4·(-75)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-50}{2*-75}=\frac{-100}{-150}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50}{2*-75}=\frac{0}{-150}
=0
$