4/7m-6=1/3m+4

Solution for 4/7m-6=1/3m+4 equation:

4/7m-6=1/3m+4

We move all terms to the left:

4/7m-6-(1/3m+4)=0


Domain of the equation: 7m!=0

m!=0/7

m!=0

m∈R



Domain of the equation: 3m+4)!=0

m∈R


We get rid of parentheses

4/7m-1/3m-4-6=0

We calculate fractions


12m/21m^2+(-7m)/21m^2-4-6=0

We add all the numbers together, and all the variables

12m/21m^2+(-7m)/21m^2-10=0

We multiply all the terms by the denominator


12m+(-7m)-10*21m^2=0

Wy multiply elements

-210m^2+12m+(-7m)=0

We get rid of parentheses

-210m^2+12m-7m=0

We add all the numbers together, and all the variables

-210m^2+5m=0

a = -210; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-210)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-210}=\frac{-10}{-420}
=1/42
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-210}=\frac{0}{-420}
=0
$