2/3x-1/9=4+2/5x

Solution for 2/3x-1/9=4+2/5x equation:

2/3x-1/9=4+2/5x

We move all terms to the left:

2/3x-1/9-(4+2/5x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(2/5x+4)-1/9=0

We get rid of parentheses

2/3x-2/5x-4-1/9=0

We calculate fractions


(-75x^2)/1215x^2+810x/1215x^2+(-486x)/1215x^2-4=0

We multiply all the terms by the denominator


(-75x^2)+810x+(-486x)-4*1215x^2=0

Wy multiply elements

(-75x^2)-4860x^2+810x+(-486x)=0

We get rid of parentheses

-75x^2-4860x^2+810x-486x=0

We add all the numbers together, and all the variables

-4935x^2+324x=0

a = -4935; b = 324; c = 0;
Δ = b2-4ac
Δ = 3242-4·(-4935)·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*-4935}=\frac{-648}{-9870}
=108/1645
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(324)+324}{2*-4935}=\frac{0}{-9870}
=0
$