3/5x-6=1/3x

Solution for 3/5x-6=1/3x equation:

3/5x-6=1/3x

We move all terms to the left:

3/5x-6-(1/3x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(+1/3x)-6=0

We get rid of parentheses

3/5x-1/3x-6=0

We calculate fractions


9x/15x^2+(-5x)/15x^2-6=0

We multiply all the terms by the denominator


9x+(-5x)-6*15x^2=0

Wy multiply elements

-90x^2+9x+(-5x)=0

We get rid of parentheses

-90x^2+9x-5x=0

We add all the numbers together, and all the variables

-90x^2+4x=0

a = -90; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-90)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-90}=\frac{-8}{-180}
=2/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-90}=\frac{0}{-180}
=0
$