4x/(6x+4)=x/25

Solution for 4x/(6x+4)=x/25 equation:

4x/(6x+4)=x/25

We move all terms to the left:

4x/(6x+4)-(x/25)=0


Domain of the equation: (6x+4)!=0

We move all terms containing x to the left, all other terms to the right

6x!=-4

x!=-4/6

x!=-2/3

x∈R


We add all the numbers together, and all the variables

4x/(6x+4)-(+x/25)=0

We get rid of parentheses

4x/(6x+4)-x/25=0

We calculate fractions


(-6x^2-4x)/(150x+100)+100x/(150x+100)=0

We multiply all the terms by the denominator


(-6x^2-4x)+100x=0

We get rid of parentheses

-6x^2-4x+100x=0

We add all the numbers together, and all the variables

-6x^2+96x=0

a = -6; b = 96; c = 0;
Δ = b2-4ac
Δ = 962-4·(-6)·0
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-96}{2*-6}=\frac{-192}{-12}
=+16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+96}{2*-6}=\frac{0}{-12}
=0
$