1/5m-2=3/10m

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

1/5m-2=3/10m

We move all terms to the left:

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


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R



Domain of the equation: 10m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-100m^2+10m-15m=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{0}{-200}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-100}=\frac{10}{-200}
=-1/20
$