3/5x-1/3x=4/9+1

Solution for 3/5x-1/3x=4/9+1 equation:

3/5x-1/3x=4/9+1

We move all terms to the left:

3/5x-1/3x-(4/9+1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

3/5x-1/3x-1-4/9=0

We calculate fractions


(-180x^2)/1215x^2+729x/1215x^2+(-405x)/1215x^2-1=0

We multiply all the terms by the denominator


(-180x^2)+729x+(-405x)-1*1215x^2=0

Wy multiply elements

(-180x^2)-1215x^2+729x+(-405x)=0

We get rid of parentheses

-180x^2-1215x^2+729x-405x=0

We add all the numbers together, and all the variables

-1395x^2+324x=0

a = -1395; b = 324; c = 0;
Δ = b2-4ac
Δ = 3242-4·(-1395)·0
Δ = 104976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{104976}=324$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(324)-324}{2*-1395}=\frac{-648}{-2790}
=36/155
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(324)+324}{2*-1395}=\frac{0}{-2790}
=0
$