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

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

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

We move all terms to the left:

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


Domain of the equation: 10m!=0

m!=0/10

m!=0

m∈R



Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

100m^2+5m=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:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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