2/3x+1/9x+5=20

Solution for 2/3x+1/9x+5=20 equation:

2/3x+1/9x+5=20

We move all terms to the left:

2/3x+1/9x+5-(20)=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

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

We calculate fractions


18x/27x^2+3x/27x^2-15=0

We multiply all the terms by the denominator


18x+3x-15*27x^2=0

We add all the numbers together, and all the variables

21x-15*27x^2=0

Wy multiply elements

-405x^2+21x=0

a = -405; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-405)·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*-405}=\frac{-42}{-810}
=7/135
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-405}=\frac{0}{-810}
=0
$