3+1/9x=1/5x

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

3+1/9x=1/5x

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/9x-1/5x+3=0

We calculate fractions


5x/45x^2+(-9x)/45x^2+3=0

We multiply all the terms by the denominator


5x+(-9x)+3*45x^2=0

Wy multiply elements

135x^2+5x+(-9x)=0

We get rid of parentheses

135x^2+5x-9x=0

We add all the numbers together, and all the variables

135x^2-4x=0

a = 135; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·135·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*135}=\frac{0}{270}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*135}=\frac{8}{270}
=4/135
$