1/2m+7=1/5m+1

Solution for 1/2m+7=1/5m+1 equation:

1/2m+7=1/5m+1

We move all terms to the left:

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


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 5m+1)!=0

m∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

5m/10m^2+(-2m)/10m^2+6=0

We multiply all the terms by the denominator


5m+(-2m)+6*10m^2=0

Wy multiply elements

60m^2+5m+(-2m)=0

We get rid of parentheses

60m^2+5m-2m=0

We add all the numbers together, and all the variables

60m^2+3m=0

a = 60; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·60·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*60}=\frac{-6}{120}
=-1/20
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*60}=\frac{0}{120}
=0
$