2/5x-1/5=3/10x+4

Solution for 2/5x-1/5=3/10x+4 equation:

2/5x-1/5=3/10x+4

We move all terms to the left:

2/5x-1/5-(3/10x+4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x+4)!=0

x∈R


We get rid of parentheses

2/5x-3/10x-4-1/5=0

We calculate fractions


20x/1250x^2+(-375x)/1250x^2+(-10x)/1250x^2-4=0

We multiply all the terms by the denominator


20x+(-375x)+(-10x)-4*1250x^2=0

Wy multiply elements

-5000x^2+20x+(-375x)+(-10x)=0

We get rid of parentheses

-5000x^2+20x-375x-10x=0

We add all the numbers together, and all the variables

-5000x^2-365x=0

a = -5000; b = -365; c = 0;
Δ = b2-4ac
Δ = -3652-4·(-5000)·0
Δ = 133225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{133225}=365$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-365)-365}{2*-5000}=\frac{0}{-10000}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-365)+365}{2*-5000}=\frac{730}{-10000}
=-73/1000
$