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

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

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

We move all terms to the left:

5/9x-1+2/3x-(5)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


15x/27x^2+18x/27x^2-6=0

We multiply all the terms by the denominator


15x+18x-6*27x^2=0

We add all the numbers together, and all the variables

33x-6*27x^2=0

Wy multiply elements

-162x^2+33x=0

a = -162; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·(-162)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*-162}=\frac{-66}{-324}
=11/54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*-162}=\frac{0}{-324}
=0
$