5/6m=2-11/2m

Solution for 5/6m=2-11/2m equation:

5/6m=2-11/2m

We move all terms to the left:

5/6m-(2-11/2m)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R



Domain of the equation: 2m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

5/6m-(-11/2m+2)=0

We get rid of parentheses

5/6m+11/2m-2=0

We calculate fractions


10m/12m^2+66m/12m^2-2=0

We multiply all the terms by the denominator


10m+66m-2*12m^2=0

We add all the numbers together, and all the variables

76m-2*12m^2=0

Wy multiply elements

-24m^2+76m=0

a = -24; b = 76; c = 0;
Δ = b2-4ac
Δ = 762-4·(-24)·0
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-76}{2*-24}=\frac{-152}{-48}
=3+1/6
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+76}{2*-24}=\frac{0}{-48}
=0
$