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

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

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

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 5x+3)!=0

x∈R


We get rid of parentheses

5/9x-9/5x-3-3=0

We calculate fractions


25x/45x^2+(-81x)/45x^2-3-3=0

We add all the numbers together, and all the variables

25x/45x^2+(-81x)/45x^2-6=0

We multiply all the terms by the denominator


25x+(-81x)-6*45x^2=0

Wy multiply elements

-270x^2+25x+(-81x)=0

We get rid of parentheses

-270x^2+25x-81x=0

We add all the numbers together, and all the variables

-270x^2-56x=0

a = -270; b = -56; c = 0;
Δ = b2-4ac
Δ = -562-4·(-270)·0
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-56}{2*-270}=\frac{0}{-540}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+56}{2*-270}=\frac{112}{-540}
=-28/135
$