14/15x-1/3=7/9x

Solution for 14/15x-1/3=7/9x equation:

14/15x-1/3=7/9x

We move all terms to the left:

14/15x-1/3-(7/9x)=0


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

14/15x-(+7/9x)-1/3=0

We get rid of parentheses

14/15x-7/9x-1/3=0

We calculate fractions


(-1215x^2)/1215x^2+1134x/1215x^2+(-945x)/1215x^2=0

We multiply all the terms by the denominator


(-1215x^2)+1134x+(-945x)=0

We get rid of parentheses

-1215x^2+1134x-945x=0

We add all the numbers together, and all the variables

-1215x^2+189x=0

a = -1215; b = 189; c = 0;
Δ = b2-4ac
Δ = 1892-4·(-1215)·0
Δ = 35721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{35721}=189$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(189)-189}{2*-1215}=\frac{-378}{-2430}
=7/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(189)+189}{2*-1215}=\frac{0}{-2430}
=0
$