(2/17x)+1=3/23x

Solution for (2/17x)+1=3/23x equation:

(2/17x)+1=3/23x

We move all terms to the left:

(2/17x)+1-(3/23x)=0


Domain of the equation: 17x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 23x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/17x)-(+3/23x)+1=0

We get rid of parentheses

2/17x-3/23x+1=0

We calculate fractions


46x/391x^2+(-51x)/391x^2+1=0

We multiply all the terms by the denominator


46x+(-51x)+1*391x^2=0

Wy multiply elements

391x^2+46x+(-51x)=0

We get rid of parentheses

391x^2+46x-51x=0

We add all the numbers together, and all the variables

391x^2-5x=0

a = 391; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·391·0
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*391}=\frac{0}{782}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*391}=\frac{10}{782}
=5/391
$