5/6m=3-11/12m

Solution for 5/6m=3-11/12m equation:

5/6m=3-11/12m

We move all terms to the left:

5/6m-(3-11/12m)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R



Domain of the equation: 12m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

5/6m-(-11/12m+3)=0

We get rid of parentheses

5/6m+11/12m-3=0

We calculate fractions


60m/72m^2+66m/72m^2-3=0

We multiply all the terms by the denominator


60m+66m-3*72m^2=0

We add all the numbers together, and all the variables

126m-3*72m^2=0

Wy multiply elements

-216m^2+126m=0

a = -216; b = 126; c = 0;
Δ = b2-4ac
Δ = 1262-4·(-216)·0
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-126}{2*-216}=\frac{-252}{-432}
=7/12
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+126}{2*-216}=\frac{0}{-432}
=0
$