1/5x^-1/10x+3/25=0

Solution for 1/5x^-1/10x+3/25=0 equation:

1/5x^-1/10x+3/25=0


Domain of the equation: 5x^!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We calculate fractions


150x^2/2500x^2+500x/2500x^2+(-250x)/2500x^2=0

We multiply all the terms by the denominator


150x^2+500x+(-250x)=0

We get rid of parentheses

150x^2+500x-250x=0

We add all the numbers together, and all the variables

150x^2+250x=0

a = 150; b = 250; c = 0;
Δ = b2-4ac
Δ = 2502-4·150·0
Δ = 62500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{62500}=250$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-250}{2*150}=\frac{-500}{300}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+250}{2*150}=\frac{0}{300}
=0
$