1/7m-2=3/14m+1

Solution for 1/7m-2=3/14m+1 equation:

1/7m-2=3/14m+1

We move all terms to the left:

1/7m-2-(3/14m+1)=0


Domain of the equation: 7m!=0

m!=0/7

m!=0

m∈R



Domain of the equation: 14m+1)!=0

m∈R


We get rid of parentheses

1/7m-3/14m-1-2=0

We calculate fractions


14m/98m^2+(-21m)/98m^2-1-2=0

We add all the numbers together, and all the variables

14m/98m^2+(-21m)/98m^2-3=0

We multiply all the terms by the denominator


14m+(-21m)-3*98m^2=0

Wy multiply elements

-294m^2+14m+(-21m)=0

We get rid of parentheses

-294m^2+14m-21m=0

We add all the numbers together, and all the variables

-294m^2-7m=0

a = -294; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-294)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-294}=\frac{0}{-588}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-294}=\frac{14}{-588}
=-1/42
$