2m-(6-4m)/7m-(4+m)=2/3

Solution for 2m-(6-4m)/7m-(4+m)=2/3 equation:

2m-(6-4m)/7m-(4+m)=2/3

We move all terms to the left:

2m-(6-4m)/7m-(4+m)-(2/3)=0


Domain of the equation: 7m!=0

m!=0/7

m!=0

m∈R


We add all the numbers together, and all the variables

2m-(-4m+6)/7m-(m+4)-(+2/3)=0

We get rid of parentheses

2m-(-4m+6)/7m-m-4-2/3=0

We calculate fractions


2m-m+(12m-18)/21m+(-14m)/21m-4=0

We add all the numbers together, and all the variables

m+(12m-18)/21m+(-14m)/21m-4=0

We multiply all the terms by the denominator


m*21m+(12m-18)+(-14m)-4*21m=0

Wy multiply elements

21m^2+(12m-18)+(-14m)-84m=0

We get rid of parentheses

21m^2+12m-14m-84m-18=0

We add all the numbers together, and all the variables

21m^2-86m-18=0

a = 21; b = -86; c = -18;
Δ = b2-4ac
Δ = -862-4·21·(-18)
Δ = 8908
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8908}=\sqrt{4*2227}=\sqrt{4}*\sqrt{2227}=2\sqrt{2227}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-2\sqrt{2227}}{2*21}=\frac{86-2\sqrt{2227}}{42}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+2\sqrt{2227}}{2*21}=\frac{86+2\sqrt{2227}}{42}
$