2/3x+5/6=4/9x+2

Solution for 2/3x+5/6=4/9x+2 equation:

2/3x+5/6=4/9x+2

We move all terms to the left:

2/3x+5/6-(4/9x+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-4/9x-2+5/6=0

We calculate fractions


1215x^2/972x^2+648x/972x^2+(-432x)/972x^2-2=0

We multiply all the terms by the denominator


1215x^2+648x+(-432x)-2*972x^2=0

Wy multiply elements

1215x^2-1944x^2+648x+(-432x)=0

We get rid of parentheses

1215x^2-1944x^2+648x-432x=0

We add all the numbers together, and all the variables

-729x^2+216x=0

a = -729; b = 216; c = 0;
Δ = b2-4ac
Δ = 2162-4·(-729)·0
Δ = 46656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46656}=216$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-216}{2*-729}=\frac{-432}{-1458}
=8/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+216}{2*-729}=\frac{0}{-1458}
=0
$