1/3x-3/5x=6

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

1/3x-3/5x=6

We move all terms to the left:

1/3x-3/5x-(6)=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+(-9x)/15x^2-6=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-90x^2+5x-9x=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{0}{-180}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-90}=\frac{8}{-180}
=-2/45
$