4/6m=18-2/7m

Solution for 4/6m=18-2/7m equation:

4/6m=18-2/7m

We move all terms to the left:

4/6m-(18-2/7m)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R



Domain of the equation: 7m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

4/6m-(-2/7m+18)=0

We get rid of parentheses

4/6m+2/7m-18=0

We calculate fractions


28m/42m^2+12m/42m^2-18=0

We multiply all the terms by the denominator


28m+12m-18*42m^2=0

We add all the numbers together, and all the variables

40m-18*42m^2=0

Wy multiply elements

-756m^2+40m=0

a = -756; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·(-756)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*-756}=\frac{-80}{-1512}
=10/189
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*-756}=\frac{0}{-1512}
=0
$