1/3x-1/5x=3

Solution for 1/3x-1/5x=3 equation:

1/3x-1/5x=3

We move all terms to the left:

1/3x-1/5x-(3)=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 calculate fractions


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

We multiply all the terms by the denominator


5x+(-3x)-3*15x^2=0

Wy multiply elements

-45x^2+5x+(-3x)=0

We get rid of parentheses

-45x^2+5x-3x=0

We add all the numbers together, and all the variables

-45x^2+2x=0

a = -45; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-45)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-45}=\frac{-4}{-90}
=2/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-45}=\frac{0}{-90}
=0
$