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

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

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

We move all terms to the left:

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


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


15x/50x^2+(-10x)/50x^2+2=0

We multiply all the terms by the denominator


15x+(-10x)+2*50x^2=0

Wy multiply elements

100x^2+15x+(-10x)=0

We get rid of parentheses

100x^2+15x-10x=0

We add all the numbers together, and all the variables

100x^2+5x=0

a = 100; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·100·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*100}=\frac{-10}{200}
=-1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*100}=\frac{0}{200}
=0
$