1/5x=1-3/10x

Solution for 1/5x=1-3/10x equation:

1/5x=1-3/10x

We move all terms to the left:

1/5x-(1-3/10x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(-3/10x+1)=0

We get rid of parentheses

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

We calculate fractions


10x/50x^2+15x/50x^2-1=0

We multiply all the terms by the denominator


10x+15x-1*50x^2=0

We add all the numbers together, and all the variables

25x-1*50x^2=0

Wy multiply elements

-50x^2+25x=0

a = -50; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-50)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-50}=\frac{-50}{-100}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-50}=\frac{0}{-100}
=0
$