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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

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

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

We calculate fractions


9x/27x^2+12x/27x^2+4=0

We multiply all the terms by the denominator


9x+12x+4*27x^2=0

We add all the numbers together, and all the variables

21x+4*27x^2=0

Wy multiply elements

108x^2+21x=0

a = 108; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·108·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*108}=\frac{-42}{216}
=-7/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*108}=\frac{0}{216}
=0
$