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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


(-24m^2+36m)/21m-3m+(-14m)/21m-4=0

We multiply all the terms by the denominator


(-24m^2+36m)-3m*21m+(-14m)-4*21m=0

Wy multiply elements

(-24m^2+36m)-63m^2+(-14m)-84m=0

We get rid of parentheses

-24m^2-63m^2+36m-14m-84m=0

We add all the numbers together, and all the variables

-87m^2-62m=0

a = -87; b = -62; c = 0;
Δ = b2-4ac
Δ = -622-4·(-87)·0
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-62}{2*-87}=\frac{0}{-174}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+62}{2*-87}=\frac{124}{-174}
=-62/87
$