5/7m-1/3m=6

Solution for 5/7m-1/3m=6 equation:

5/7m-1/3m=6

We move all terms to the left:

5/7m-1/3m-(6)=0


Domain of the equation: 7m!=0

m!=0/7

m!=0

m∈R



Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We calculate fractions


15m/21m^2+(-7m)/21m^2-6=0

We multiply all the terms by the denominator


15m+(-7m)-6*21m^2=0

Wy multiply elements

-126m^2+15m+(-7m)=0

We get rid of parentheses

-126m^2+15m-7m=0

We add all the numbers together, and all the variables

-126m^2+8m=0

a = -126; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-126)·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*-126}=\frac{-16}{-252}
=4/63
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-126}=\frac{0}{-252}
=0
$