5/6x-2=3/7x-1

Solution for 5/6x-2=3/7x-1 equation:

5/6x-2=3/7x-1

We move all terms to the left:

5/6x-2-(3/7x-1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 7x-1)!=0

x∈R


We get rid of parentheses

5/6x-3/7x+1-2=0

We calculate fractions


35x/42x^2+(-18x)/42x^2+1-2=0

We add all the numbers together, and all the variables

35x/42x^2+(-18x)/42x^2-1=0

We multiply all the terms by the denominator


35x+(-18x)-1*42x^2=0

Wy multiply elements

-42x^2+35x+(-18x)=0

We get rid of parentheses

-42x^2+35x-18x=0

We add all the numbers together, and all the variables

-42x^2+17x=0

a = -42; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-42)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-42}=\frac{-34}{-84}
=17/42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-42}=\frac{0}{-84}
=0
$