4/6x-2/9x=-4

Solution for 4/6x-2/9x=-4 equation:

4/6x-2/9x=-4

We move all terms to the left:

4/6x-2/9x-(-4)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

4/6x-2/9x+4=0

We calculate fractions


36x/54x^2+(-12x)/54x^2+4=0

We multiply all the terms by the denominator


36x+(-12x)+4*54x^2=0

Wy multiply elements

216x^2+36x+(-12x)=0

We get rid of parentheses

216x^2+36x-12x=0

We add all the numbers together, and all the variables

216x^2+24x=0

a = 216; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·216·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*216}=\frac{-48}{432}
=-1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*216}=\frac{0}{432}
=0
$