2/3x-8/15=1/9x+2

Solution for 2/3x-8/15=1/9x+2 equation:

2/3x-8/15=1/9x+2

We move all terms to the left:

2/3x-8/15-(1/9x+2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x+2)!=0

x∈R


We get rid of parentheses

2/3x-1/9x-2-8/15=0

We calculate fractions


(-1944x^2)/405x^2+270x/405x^2+(-45x)/405x^2-2=0

We multiply all the terms by the denominator


(-1944x^2)+270x+(-45x)-2*405x^2=0

Wy multiply elements

(-1944x^2)-810x^2+270x+(-45x)=0

We get rid of parentheses

-1944x^2-810x^2+270x-45x=0

We add all the numbers together, and all the variables

-2754x^2+225x=0

a = -2754; b = 225; c = 0;
Δ = b2-4ac
Δ = 2252-4·(-2754)·0
Δ = 50625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{50625}=225$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(225)-225}{2*-2754}=\frac{-450}{-5508}
=25/306
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(225)+225}{2*-2754}=\frac{0}{-5508}
=0
$