3/5x=1+2/25x

Solution for 3/5x=1+2/25x equation:

3/5x=1+2/25x

We move all terms to the left:

3/5x-(1+2/25x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 25x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(2/25x+1)=0

We get rid of parentheses

3/5x-2/25x-1=0

We calculate fractions


75x/125x^2+(-10x)/125x^2-1=0

We multiply all the terms by the denominator


75x+(-10x)-1*125x^2=0

Wy multiply elements

-125x^2+75x+(-10x)=0

We get rid of parentheses

-125x^2+75x-10x=0

We add all the numbers together, and all the variables

-125x^2+65x=0

a = -125; b = 65; c = 0;
Δ = b2-4ac
Δ = 652-4·(-125)·0
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-65}{2*-125}=\frac{-130}{-250}
=13/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+65}{2*-125}=\frac{0}{-250}
=0
$