25/19x-1=8/6x

Solution for 25/19x-1=8/6x equation:

25/19x-1=8/6x

We move all terms to the left:

25/19x-1-(8/6x)=0


Domain of the equation: 19x!=0

x!=0/19

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

25/19x-(+8/6x)-1=0

We get rid of parentheses

25/19x-8/6x-1=0

We calculate fractions


150x/114x^2+(-152x)/114x^2-1=0

We multiply all the terms by the denominator


150x+(-152x)-1*114x^2=0

Wy multiply elements

-114x^2+150x+(-152x)=0

We get rid of parentheses

-114x^2+150x-152x=0

We add all the numbers together, and all the variables

-114x^2-2x=0

a = -114; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-114)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-114}=\frac{0}{-228}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-114}=\frac{4}{-228}
=-1/57
$