14/17+13/34x=17+6/68x

Solution for 14/17+13/34x=17+6/68x equation:

14/17+13/34x=17+6/68x

We move all terms to the left:

14/17+13/34x-(17+6/68x)=0


Domain of the equation: 34x!=0

x!=0/34

x!=0

x∈R



Domain of the equation: 68x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

13/34x-(6/68x+17)+14/17=0

We get rid of parentheses

13/34x-6/68x-17+14/17=0

We calculate fractions


194208x^2/39304x^2+15028x/39304x^2+(-3468x)/39304x^2-17=0

We multiply all the terms by the denominator


194208x^2+15028x+(-3468x)-17*39304x^2=0

Wy multiply elements

194208x^2-668168x^2+15028x+(-3468x)=0

We get rid of parentheses

194208x^2-668168x^2+15028x-3468x=0

We add all the numbers together, and all the variables

-473960x^2+11560x=0

a = -473960; b = 11560; c = 0;
Δ = b2-4ac
Δ = 115602-4·(-473960)·0
Δ = 133633600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{133633600}=11560$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11560)-11560}{2*-473960}=\frac{-23120}{-947920}
=1/41
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11560)+11560}{2*-473960}=\frac{0}{-947920}
=0
$