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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


72x^2/486x^2+(-243x)/486x^2+324x/486x^2=0

We multiply all the terms by the denominator


72x^2+(-243x)+324x=0

We add all the numbers together, and all the variables

72x^2+324x+(-243x)=0

We get rid of parentheses

72x^2+324x-243x=0

We add all the numbers together, and all the variables

72x^2+81x=0

a = 72; b = 81; c = 0;
Δ = b2-4ac
Δ = 812-4·72·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-81}{2*72}=\frac{-162}{144}
=-1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+81}{2*72}=\frac{0}{144}
=0
$