1/3m+2=5/7m

Solution for 1/3m+2=5/7m equation:

1/3m+2=5/7m

We move all terms to the left:

1/3m+2-(5/7m)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 7m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

1/3m-(+5/7m)+2=0

We get rid of parentheses

1/3m-5/7m+2=0

We calculate fractions


7m/21m^2+(-15m)/21m^2+2=0

We multiply all the terms by the denominator


7m+(-15m)+2*21m^2=0

Wy multiply elements

42m^2+7m+(-15m)=0

We get rid of parentheses

42m^2+7m-15m=0

We add all the numbers together, and all the variables

42m^2-8m=0

a = 42; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·42·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*42}=\frac{0}{84}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*42}=\frac{16}{84}
=4/21
$