2/13x+9=3/17x

Solution for 2/13x+9=3/17x equation:

2/13x+9=3/17x

We move all terms to the left:

2/13x+9-(3/17x)=0


Domain of the equation: 13x!=0

x!=0/13

x!=0

x∈R



Domain of the equation: 17x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/13x-(+3/17x)+9=0

We get rid of parentheses

2/13x-3/17x+9=0

We calculate fractions


34x/221x^2+(-39x)/221x^2+9=0

We multiply all the terms by the denominator


34x+(-39x)+9*221x^2=0

Wy multiply elements

1989x^2+34x+(-39x)=0

We get rid of parentheses

1989x^2+34x-39x=0

We add all the numbers together, and all the variables

1989x^2-5x=0

a = 1989; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·1989·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*1989}=\frac{0}{3978}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*1989}=\frac{10}{3978}
=5/1989
$