3+1/9x=1/13x

Solution for 3+1/9x=1/13x equation:

3+1/9x=1/13x

We move all terms to the left:

3+1/9x-(1/13x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 13x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/9x-(+1/13x)+3=0

We get rid of parentheses

1/9x-1/13x+3=0

We calculate fractions


13x/117x^2+(-9x)/117x^2+3=0

We multiply all the terms by the denominator


13x+(-9x)+3*117x^2=0

Wy multiply elements

351x^2+13x+(-9x)=0

We get rid of parentheses

351x^2+13x-9x=0

We add all the numbers together, and all the variables

351x^2+4x=0

a = 351; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·351·0
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*351}=\frac{-8}{702}
=-4/351
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*351}=\frac{0}{702}
=0
$