4/5x-1=5/9x+2

Solution for 4/5x-1=5/9x+2 equation:

4/5x-1=5/9x+2

We move all terms to the left:

4/5x-1-(5/9x+2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 9x+2)!=0

x∈R


We get rid of parentheses

4/5x-5/9x-2-1=0

We calculate fractions


36x/45x^2+(-25x)/45x^2-2-1=0

We add all the numbers together, and all the variables

36x/45x^2+(-25x)/45x^2-3=0

We multiply all the terms by the denominator


36x+(-25x)-3*45x^2=0

Wy multiply elements

-135x^2+36x+(-25x)=0

We get rid of parentheses

-135x^2+36x-25x=0

We add all the numbers together, and all the variables

-135x^2+11x=0

a = -135; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-135)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-135}=\frac{-22}{-270}
=11/135
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-135}=\frac{0}{-270}
=0
$