38/2x-1=60/4x-26

Solution for 38/2x-1=60/4x-26 equation:

38/2x-1=60/4x-26

We move all terms to the left:

38/2x-1-(60/4x-26)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-26)!=0

x∈R


We get rid of parentheses

38/2x-60/4x+26-1=0

We calculate fractions


152x/8x^2+(-120x)/8x^2+26-1=0

We add all the numbers together, and all the variables

152x/8x^2+(-120x)/8x^2+25=0

We multiply all the terms by the denominator


152x+(-120x)+25*8x^2=0

Wy multiply elements

200x^2+152x+(-120x)=0

We get rid of parentheses

200x^2+152x-120x=0

We add all the numbers together, and all the variables

200x^2+32x=0

a = 200; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·200·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*200}=\frac{-64}{400}
=-4/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*200}=\frac{0}{400}
=0
$