2/5m-7=1/10m

Solution for 2/5m-7=1/10m equation:

2/5m-7=1/10m

We move all terms to the left:

2/5m-7-(1/10m)=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

2/5m-(+1/10m)-7=0

We get rid of parentheses

2/5m-1/10m-7=0

We calculate fractions


20m/50m^2+(-5m)/50m^2-7=0

We multiply all the terms by the denominator


20m+(-5m)-7*50m^2=0

Wy multiply elements

-350m^2+20m+(-5m)=0

We get rid of parentheses

-350m^2+20m-5m=0

We add all the numbers together, and all the variables

-350m^2+15m=0

a = -350; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-350)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-350}=\frac{-30}{-700}
=3/70
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-350}=\frac{0}{-700}
=0
$