1/5x-2/5=3/10x+1

Solution for 1/5x-2/5=3/10x+1 equation:

1/5x-2/5=3/10x+1

We move all terms to the left:

1/5x-2/5-(3/10x+1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x+1)!=0

x∈R


We get rid of parentheses

1/5x-3/10x-1-2/5=0

We calculate fractions


10x/1250x^2+(-375x)/1250x^2+(-20x)/1250x^2-1=0

We multiply all the terms by the denominator


10x+(-375x)+(-20x)-1*1250x^2=0

Wy multiply elements

-1250x^2+10x+(-375x)+(-20x)=0

We get rid of parentheses

-1250x^2+10x-375x-20x=0

We add all the numbers together, and all the variables

-1250x^2-385x=0

a = -1250; b = -385; c = 0;
Δ = b2-4ac
Δ = -3852-4·(-1250)·0
Δ = 148225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{148225}=385$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-385)-385}{2*-1250}=\frac{0}{-2500}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-385)+385}{2*-1250}=\frac{770}{-2500}
=-77/250
$